Belmont, Eva; Shimomura, Katsumi Beta families arising from a \(v_2^9\) self-map on \(S/(3, v_1^8)\). (English) Zbl 07775435 Algebr. Geom. Topol. 23, No. 9, 4349-4378 (2023). MSC: 55Q45 55Q51 55T25 PDFBibTeX XMLCite \textit{E. Belmont} and \textit{K. Shimomura}, Algebr. Geom. Topol. 23, No. 9, 4349--4378 (2023; Zbl 07775435) Full Text: DOI arXiv
Shimomura, Katsumi A relation among Hopkins’ Picard groups of the localized categories with respect to finite wedges of the Morava \(K\)-theories. (English) Zbl 07578596 Trans. Am. Math. Soc. 375, No. 9, 6337-6361 (2022). MSC: 55P42 55P43 55Q99 55T99 PDFBibTeX XMLCite \textit{K. Shimomura}, Trans. Am. Math. Soc. 375, No. 9, 6337--6361 (2022; Zbl 07578596) Full Text: DOI
Ichigi, Ippei; Shimomura, Katsumi On the Picard group graded homotopy groups of a finite type two \(K(2)\)-local spectrum at the prime three. (English) Zbl 1493.55013 Homology Homotopy Appl. 24, No. 1, 177-203 (2022). Reviewer: Steffen Sagave (Nijmegen) MSC: 55P42 55Q51 55Q52 55T15 PDFBibTeX XMLCite \textit{I. Ichigi} and \textit{K. Shimomura}, Homology Homotopy Appl. 24, No. 1, 177--203 (2022; Zbl 1493.55013) Full Text: DOI
Kato, Ryo; Shimomura, Katsumi A note on products in stable homotopy groups of spheres via the classical Adams spectral sequence. (English) Zbl 1458.55009 Math. J. Okayama Univ. 63, 107-122 (2021). Reviewer: Jianbo Wang (Tianjin) MSC: 55Q45 55T15 PDFBibTeX XMLCite \textit{R. Kato} and \textit{K. Shimomura}, Math. J. Okayama Univ. 63, 107--122 (2021; Zbl 1458.55009) Full Text: Link
Kato, Ryo; Okajima, Hiroki; Shimomura, Katsumi Notes on an algebraic stable homotopy category. (English) Zbl 1480.55019 Ohsawa, Takeo (ed.) et al., Bousfield classes and Ohkawa’s theorem. Selected contributions given at the workshop, Nagoya, Japan, August 28–30, 2015. Singapore: Springer. Springer Proc. Math. Stat. 309, 103-108 (2020). MSC: 55U35 55P42 18G80 18M05 18N40 PDFBibTeX XMLCite \textit{R. Kato} et al., Springer Proc. Math. Stat. 309, 103--108 (2020; Zbl 1480.55019) Full Text: DOI
Shimomura, Katsumi A note on Hopkins’ Picard groups of the stable homotopy categories of \(L_n\)-local spectra. (English) Zbl 1442.55009 Publ. Res. Inst. Math. Sci. 56, No. 1, 195-205 (2020). Reviewer: Luca Pol (Sheffield) MSC: 55P99 55P42 55P60 PDFBibTeX XMLCite \textit{K. Shimomura}, Publ. Res. Inst. Math. Sci. 56, No. 1, 195--205 (2020; Zbl 1442.55009) Full Text: DOI
Okajima, Hiroki; Shimomura, Katsumi A note on the products \(\alpha_1\beta_2\gamma_t\) and \(\beta_1^{r+1}\beta_2\gamma_t\) in the stable homotopy of spheres. (English) Zbl 1509.55009 Hiroshima Math. J. 49, No. 3, 303-321 (2019). Reviewer: Jianbo Wang (Tianjin) MSC: 55Q45 55T15 55Q51 PDFBibTeX XMLCite \textit{H. Okajima} and \textit{K. Shimomura}, Hiroshima Math. J. 49, No. 3, 303--321 (2019; Zbl 1509.55009) Full Text: DOI Euclid
Kato, Ryo; Shimomura, Katsumi; Tatehara, Yutaro Generalized Bousfield lattices and a generalized retract conjecture. (English) Zbl 1305.55006 Publ. Res. Inst. Math. Sci. 50, No. 3, 497-513 (2014). Reviewer: Friedrich Wilhelm Bauer (Frankfurt am Main) MSC: 55P42 06D75 PDFBibTeX XMLCite \textit{R. Kato} et al., Publ. Res. Inst. Math. Sci. 50, No. 3, 497--513 (2014; Zbl 1305.55006) Full Text: DOI
Shimomura, Katsumi A beta family in the homotopy of spheres. (English) Zbl 1310.55008 Proc. Am. Math. Soc. 142, No. 8, 2921-2928 (2014). Reviewer: Alice Kimie Miwa Libardi (Sao Paulo) MSC: 55Q45 55Q51 PDFBibTeX XMLCite \textit{K. Shimomura}, Proc. Am. Math. Soc. 142, No. 8, 2921--2928 (2014; Zbl 1310.55008) Full Text: DOI
Shimomura, Katsumi; Yoshizawa, Kié On the product \({\alpha}_1, {\beta}^r_1, {\gamma}_t\) in the stable homotopy groups of spheres. (English) Zbl 1300.55017 Kochi J. Math. 9, 169-172 (2014). MSC: 55Q45 PDFBibTeX XMLCite \textit{K. Shimomura} and \textit{K. Yoshizawa}, Kochi J. Math. 9, 169--172 (2014; Zbl 1300.55017)
Kato, Ryo; Shimomura, Katsumi The first line of the Bockstein spectral sequence on a monochromatic spectrum at an odd prime. (English) Zbl 1277.55007 Nagoya Math. J. 207, 139-157 (2012). Reviewer: Daniel G. Davis (Lafayette) MSC: 55Q99 55T99 55Q45 PDFBibTeX XMLCite \textit{R. Kato} and \textit{K. Shimomura}, Nagoya Math. J. 207, 139--157 (2012; Zbl 1277.55007) Full Text: arXiv Euclid
Shimomura, Katsumi; Tokashiki, Shingo On the cohomology of \(S (n,n - 1)\) relevant to the Morava stabilizer algebra at a prime \(> 3\). (English) Zbl 1271.55012 Kochi J. Math. 7, 109-118 (2012). Reviewer: Marek Golasiński (Olsztyn) MSC: 55Q10 20J06 55Q51 PDFBibTeX XMLCite \textit{K. Shimomura} and \textit{S. Tokashiki}, Kochi J. Math. 7, 109--118 (2012; Zbl 1271.55012)
Kato, Ryo; Shimomura, Katsumi Products of Greek letter elements dug up from the third Morava stabilizer algebra. (English) Zbl 1245.55005 Algebr. Geom. Topol. 12, No. 2, 951-961 (2012). Reviewer: Liu Xiugui (Tianjing) MSC: 55Q45 55Q51 PDFBibTeX XMLCite \textit{R. Kato} and \textit{K. Shimomura}, Algebr. Geom. Topol. 12, No. 2, 951--961 (2012; Zbl 1245.55005) Full Text: DOI arXiv
Kitahama, Rié; Shimomura, Katsumi On the chromatic Ext\(^0(M^1_{n-1})\) on \(\Gamma(m+1)\) for an odd prime. (English) Zbl 1234.55014 Hiroshima Math. J. 41, No. 2, 211-222 (2011). Reviewer: Katsumi Shimomura (Kochi) MSC: 55T15 55Q45 55Q51 PDFBibTeX XMLCite \textit{R. Kitahama} and \textit{K. Shimomura}, Hiroshima Math. J. 41, No. 2, 211--222 (2011; Zbl 1234.55014) Full Text: Euclid
Ichigi, Ippei; Shimomura, Katsumi; Takeda, Rinko The homotopy groups of \(L_2\)-localization of the Ravenel spectra \(T(m)/\upsilon_1\) at the prime two. (English) Zbl 1254.55010 Bol. Soc. Mat. Mex., III. Ser. 16, No. 1, 53-61 (2010). Reviewer: Liu Xiugui (Tianjing) MSC: 55Q45 55Q99 55Q51 PDFBibTeX XMLCite \textit{I. Ichigi} et al., Bol. Soc. Mat. Mex., III. Ser. 16, No. 1, 53--61 (2010; Zbl 1254.55010) Full Text: Link
Shimomura, Katsumi The beta elements \(\beta_{tp^2/r}\) in the homotopy of spheres. (English) Zbl 1223.55007 Algebr. Geom. Topol. 10, No. 4, 2079-2090 (2010). Reviewer: Younggi Choi (Seoul) MSC: 55Q45 55Q10 55T15 PDFBibTeX XMLCite \textit{K. Shimomura}, Algebr. Geom. Topol. 10, No. 4, 2079--2090 (2010; Zbl 1223.55007) Full Text: DOI
Shimomura, Katsumi Note on beta elements in homotopy, and an application to the prime three case. (English) Zbl 1207.55013 Proc. Am. Math. Soc. 138, No. 4, 1495-1499 (2010). Reviewer: Liu Xiugui (Tianjing) MSC: 55Q45 55T15 PDFBibTeX XMLCite \textit{K. Shimomura}, Proc. Am. Math. Soc. 138, No. 4, 1495--1499 (2010; Zbl 1207.55013) Full Text: DOI
Ichigi, Ippei; Shimomura, Katsumi The homotopy groups of the \(L_{2}\)-localization of the modulo \(p\) Moore spectrum smashing with the first Ravenel spectrum. (English) Zbl 1207.55014 Asian-Eur. J. Math. 3, No. 1, 107-118 (2010). Reviewer: Bernard Badzioch (Buffalo) MSC: 55Q51 55P60 PDFBibTeX XMLCite \textit{I. Ichigi} and \textit{K. Shimomura}, Asian-Eur. J. Math. 3, No. 1, 107--118 (2010; Zbl 1207.55014) Full Text: DOI
Ichigi, Ippei; Shimomura, Katsumi The modulo two homotopy groups of the \(L_2\)-localization of the Ravenel spectrum. (English) Zbl 1156.55011 Cubo 10, No. 3, 43-55 (2008). Reviewer: Yves Félix (Louvain-La-Neuve) MSC: 55Q99 55Q51 20J06 PDFBibTeX XMLCite \textit{I. Ichigi} and \textit{K. Shimomura}, Cubo 10, No. 3, 43--55 (2008; Zbl 1156.55011)
Nakai, Hirofumi; Shimomura, Katsumi On the homotopy groups of \(E(n)\)-local spectra with unusual invariant ideals. (English) Zbl 1258.55009 Ando, Matthew (ed.) et al., Proceedings of the Nishida Fest conferences on homotopy theory, Kinosaki, Japan, July 28–August 1 2003 and August 4–8, 2003. Dedicated to Gôrô Nishida on the occasion of his 60th birthday. Coventry: Geometry & Topology Publications. Geometry and Topology Monographs 10, 319-332 (2007). MSC: 55Q52 55P42 55T15 PDFBibTeX XMLCite \textit{H. Nakai} and \textit{K. Shimomura}, Geom. Topol. Monogr. 10, 319--332 (2007; Zbl 1258.55009) Full Text: arXiv
Ichigi, Ippei; Shimomura, Katsumi; Wang, Xiangjun On subgroups of \(\pi_*(L_2T(1)\wedge M(2))\) at the prime two. (English) Zbl 1175.55011 Bol. Soc. Mat. Mex., III. Ser. 13, No. 1, 207-230 (2007). Reviewer: Jonathan Hodgson (Philadelphia) MSC: 55Q52 55Q45 55Q51 PDFBibTeX XMLCite \textit{I. Ichigi} et al., Bol. Soc. Mat. Mex., III. Ser. 13, No. 1, 207--230 (2007; Zbl 1175.55011)
Kamiya, Yousuke; Shimomura, Katsumi Picard groups of some local categories. (English) Zbl 1136.55009 Publ. Res. Inst. Math. Sci. 43, No. 2, 303-314 (2007). Reviewer: Jie Wu (Singapore) MSC: 55P60 55P10 PDFBibTeX XMLCite \textit{Y. Kamiya} and \textit{K. Shimomura}, Publ. Res. Inst. Math. Sci. 43, No. 2, 303--314 (2007; Zbl 1136.55009) Full Text: DOI
Ichigi, Ippei; Shimomura, Katsumi Homotopy groups of generalized \(E(2)\)-local Moore spectra at the prime three. (English) Zbl 1085.55011 Hiroshima Math. J. 35, No. 1, 125-142 (2005). Reviewer: Gerd Laures (Bochum) MSC: 55Q99 55Q52 55P42 PDFBibTeX XMLCite \textit{I. Ichigi} and \textit{K. Shimomura}, Hiroshima Math. J. 35, No. 1, 125--142 (2005; Zbl 1085.55011)
Kamiya, Yousuke; Shimomura, Katsumi A relation between the Picard group of the \(E(n)\)-local homotopy category and \(E(n)\)-based Adams spectral sequence. (English) Zbl 1097.55007 Goerss, Paul (ed.) et al., Homotopy theory: relations with algebraic geometry, group cohomology, and algebraic \(K\)-theory. Papers from the international conference on algebraic topology, Northwestern University, Evanston, IL, USA, March 24–28, 2002. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-3285-9/pbk). Contemporary Mathematics 346, 321-333 (2004). Reviewer: Friedrich Wilhelm Bauer (Frankfurt a. M.) MSC: 55P42 55Q99 55P60 55T15 PDFBibTeX XMLCite \textit{Y. Kamiya} and \textit{K. Shimomura}, Contemp. Math. 346, 321--333 (2004; Zbl 1097.55007)
Ichigi, Ippei; Shimomura, Katsumi \(E(2)\)-invertible spectra smashing with the Smith-Toda spectrum \(V(1)\) at the prime \(3\). (English) Zbl 1051.55007 Proc. Am. Math. Soc. 132, No. 10, 3111-3119 (2004). Reviewer: Friedrich Wilhelm Bauer (Frankfurt a. M.) MSC: 55Q99 55Q45 55Q51 PDFBibTeX XMLCite \textit{I. Ichigi} and \textit{K. Shimomura}, Proc. Am. Math. Soc. 132, No. 10, 3111--3119 (2004; Zbl 1051.55007) Full Text: DOI
Ichigi, Ippei; Shimomura, Katsumi Subgroups of \(\pi_* (L_2T(1))\) at the prime two. (English) Zbl 1063.55012 Hiroshima Math. J. 33, No. 3, 359-369 (2003). Reviewer: Keith Johnson (Halifax) MSC: 55Q99 55Q45 55Q51 PDFBibTeX XMLCite \textit{I. Ichigi} and \textit{K. Shimomura}, Hiroshima Math. J. 33, No. 3, 359--369 (2003; Zbl 1063.55012)
Ichigi, Ippei; Shimomura, Katsumi On the homotopy groups of an invertible spectrum in the \(E(2)\)-local category at the prime 3. (English) Zbl 1050.55005 JP J. Geom. Topol. 3, No. 3, 257-268 (2003). Reviewer: J. Remedios (La Laguna) MSC: 55P42 55Q05 55Q99 55P43 55P60 PDFBibTeX XMLCite \textit{I. Ichigi} and \textit{K. Shimomura}, JP J. Geom. Topol. 3, No. 3, 257--268 (2003; Zbl 1050.55005)
Kamiya, Yousuke; Shimomura, Katsumi \(E_*\)-homology spheres for a connective spectrum \(E\). (English) Zbl 1026.55015 Berrick, A. J. (ed.) et al., Topology and geometry: commemorating SISTAG. Proceedings of the Singapore international symposium in topology and geometry (SISTAG), Singapore, July 2-6, 2001. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 314, 153-159 (2002). Reviewer: Gerd Laures (Heidelberg) MSC: 55P43 55P60 55P65 PDFBibTeX XMLCite \textit{Y. Kamiya} and \textit{K. Shimomura}, Contemp. Math. 314, 153--159 (2002; Zbl 1026.55015)
Shimomura, Katsumi; Wang, Xiangjun The homotopy groups \(\pi_*(L_2 S^0)\) at the prime 3. (English) Zbl 1007.55007 Topology 41, No. 6, 1183-1198 (2002). Reviewer: Jonathan Hodgson (Philadelphia) MSC: 55Q40 55Q52 55T15 PDFBibTeX XMLCite \textit{K. Shimomura} and \textit{X. Wang}, Topology 41, No. 6, 1183--1198 (2002; Zbl 1007.55007) Full Text: DOI
Shimomura, Katsumi; Wang, Xiangjun The Adams-Novikov \(E_2\)-term for \(\pi_*(L_2S^0)\) at the prime 2. (English) Zbl 1012.55021 Math. Z. 241, No. 2, 271-311 (2002). Reviewer: Michael Joachim (Münster) MSC: 55Q45 55T15 55P42 55P60 55Q10 PDFBibTeX XMLCite \textit{K. Shimomura} and \textit{X. Wang}, Math. Z. 241, No. 2, 271--311 (2002; Zbl 1012.55021) Full Text: DOI
Shimomura, Katsumi The homotopy groups \(\pi_*(L_nT(m)\wedge V(n-2))\). (English) Zbl 1012.55020 Davis, Donald M. (ed.) et al., Recent progress in homotopy theory. Proceedings of a conference, Baltimore, MD, USA, March 17-27, 2000. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 293, 285-297 (2002). Reviewer: Victor P.Snaith (Southampton) MSC: 55Q10 55Q51 55Q45 PDFBibTeX XMLCite \textit{K. Shimomura}, Contemp. Math. 293, 285--297 (2002; Zbl 1012.55020)
Kamiya, Yousuke; Shimomura, Katsumi The homotopy groups \(\pi_*(L_2V(0) \wedge T(k))\). (English) Zbl 1004.55007 Hiroshima Math. J. 31, No. 3, 391-408 (2001). Reviewer: C.A.Robinson (Coventry) MSC: 55Q51 55Q10 PDFBibTeX XMLCite \textit{Y. Kamiya} and \textit{K. Shimomura}, Hiroshima Math. J. 31, No. 3, 391--408 (2001; Zbl 1004.55007)
Shimomura, Katsumi On the action of \(\beta_1\) in the stable homotopy of spheres at the prime 3. (English) Zbl 0997.55017 Hiroshima Math. J. 30, No. 2, 345-362 (2000). Reviewer: A.J.Baker (Glasgow) MSC: 55Q45 55Q51 55Q10 PDFBibTeX XMLCite \textit{K. Shimomura}, Hiroshima Math. J. 30, No. 2, 345--362 (2000; Zbl 0997.55017)
Ichigi, Ippei; Shimomura, Katsumi The chromatic \(E_1\)-term \(\text{Ext}^0 (v_3^{-1} BP_* / (3, v_1, v_2^{\infty}) [t_1])\). (English) Zbl 0946.55013 Mem. Fac. Sci., Kochi Univ., Ser. A 21, 63-71 (2000). Reviewer: Keith Johnson (Halifax) MSC: 55T15 55Q51 55P42 PDFBibTeX XMLCite \textit{I. Ichigi} and \textit{K. Shimomura}, Mem. Fac. Sci., Kochi Univ., Ser. A 21, 63--71 (2000; Zbl 0946.55013)
Shimomura, Katsumi The homotopy groups of the \(L_2\)-localized mod 3 Moore spectrum. (English) Zbl 0946.55006 J. Math. Soc. Japan 52, No. 1, 65-90 (2000). Reviewer: K.Shimomura (Kochi) MSC: 55Q45 55T15 55P43 55Q52 55P42 PDFBibTeX XMLCite \textit{K. Shimomura}, J. Math. Soc. Japan 52, No. 1, 65--90 (2000; Zbl 0946.55006) Full Text: DOI
Shimomura, Katsumi The Adams-Novikov \(E_2\)-term for computing \(\pi_*(L_2 V(0))\) at the prime 2. (English) Zbl 0931.55009 Topology Appl. 96, No. 2, 133-152 (1999). Reviewer: Michael Joachim (Münster) MSC: 55Q10 55T15 55Q45 55P60 PDFBibTeX XMLCite \textit{K. Shimomura}, Topology Appl. 96, No. 2, 133--152 (1999; Zbl 0931.55009) Full Text: DOI
Shimomura, Katsumi The homotopy groups of an \(L_2\)-localized type one finite spectrum at the prime 2. (English) Zbl 0902.55005 Hiroshima Math. J. 28, No. 1, 113-127 (1998). Reviewer: D.Davis (Bethlehem) MSC: 55Q10 55T15 55Q45 55P60 PDFBibTeX XMLCite \textit{K. Shimomura}, Hiroshima Math. J. 28, No. 1, 113--127 (1998; Zbl 0902.55005)
Arita, Yoshiko; Shimomura, Katsumi On products of some \(\beta\)-elements in the homotopy of the \(\mod 3\) Moore spectrum. (English) Zbl 0899.55014 Hiroshima Math. J. 27, No. 3, 477-486 (1997). Reviewer: S.Thomeier (St.John’s) MSC: 55Q10 55Q52 55T15 55P42 PDFBibTeX XMLCite \textit{Y. Arita} and \textit{K. Shimomura}, Hiroshima Math. J. 27, No. 3, 477--486 (1997; Zbl 0899.55014)
Nakazawa, Yoshitaka; Shimomura, Katsumi The homotopy groups of the \(L_ 2\)-localization of a certain type one finite complex at the prime 3. (English) Zbl 0880.55010 Fundam. Math. 152, No. 1, 1-20 (1997). Reviewer: Katsumi Shimomura (Kochi) MSC: 55Q10 55Q45 55P60 PDFBibTeX XMLCite \textit{Y. Nakazawa} and \textit{K. Shimomura}, Fundam. Math. 152, No. 1, 1--20 (1997; Zbl 0880.55010) Full Text: EuDML
Shimomura, Katsumi The homotopy groups of the \(L_ 2\)-localized Toda-Smith spectrum \(V(1)\) at the prime 3. (English) Zbl 0869.55012 Trans. Am. Math. Soc. 349, No. 5, 1821-1850 (1997). MSC: 55Q45 55Q10 55Q52 PDFBibTeX XMLCite \textit{K. Shimomura}, Trans. Am. Math. Soc. 349, No. 5, 1821--1850 (1997; Zbl 0869.55012) Full Text: DOI
Arita, Yoshiko; Shimomura, Katsumi The chromatic \(E_ 1\)-term \(H^ 1M_ 1^ 1\) at the prime 3. (English) Zbl 0869.55010 Hiroshima Math. J. 26, No. 2, 415-431 (1996). Reviewer: J.P.E.Hodgson (Philadelphia) MSC: 55Q10 55T99 55Q45 PDFBibTeX XMLCite \textit{Y. Arita} and \textit{K. Shimomura}, Hiroshima Math. J. 26, No. 2, 415--431 (1996; Zbl 0869.55010)
Shimomura, Katsumi 3-primary \(\beta\)-family in stable homotopy of a finite spectrum. (English) Zbl 0869.55011 Hiroshima Math. J. 26, No. 2, 341-349 (1996). Reviewer: J.P.E.Hodgson (Philadelphia) MSC: 55Q10 55Q45 PDFBibTeX XMLCite \textit{K. Shimomura}, Hiroshima Math. J. 26, No. 2, 341--349 (1996; Zbl 0869.55011)
Masamoto, Keiko; Matsuhisa, Tsuyoshi; Shimomura, Katsumi The homotopy groups of a spectrum whose \(BP_ *\)-homology is \(v_ 2^{-1} BP_ * I(2,v_ 1^ \infty)[t_ 1]\otimes \Lambda(t_ 2)\). (English) Zbl 0856.55013 Osaka J. Math. 33, No. 1, 69-82 (1996). Reviewer: D.Davis (Bethlehem) MSC: 55T15 55Q10 PDFBibTeX XMLCite \textit{K. Masamoto} et al., Osaka J. Math. 33, No. 1, 69--82 (1996; Zbl 0856.55013)
Shimomura, Katsumi The products \(\beta_ s\beta_{tp}/p\) in the stable homotopy of \(L_ 2\)-localized spheres. (English) Zbl 0862.55010 Hiroshima Math. J. 25, No. 3, 487-491 (1995). Reviewer: S.O.Kochman (Downsview) MSC: 55Q45 PDFBibTeX XMLCite \textit{K. Shimomura}, Hiroshima Math. J. 25, No. 3, 487--491 (1995; Zbl 0862.55010)
Otsubo, Reiko; Shimomura, Katsumi On some products of \(\beta\)-elements in the stable homotopy of \(L_ 2\)-local spheres. (English) Zbl 0859.55014 Kodai Math. J. 18, No. 2, 234-241 (1995). Reviewer: S.O.Kochman (Downsview) MSC: 55Q45 PDFBibTeX XMLCite \textit{R. Otsubo} and \textit{K. Shimomura}, Kodai Math. J. 18, No. 2, 234--241 (1995; Zbl 0859.55014) Full Text: DOI
Shimomura, Katsumi The homotopy groups of the \(L_ 2\)-localized Mahowald spectrum \(X\langle 1\rangle\). (English) Zbl 0835.55009 Forum Math. 7, No. 6, 685-707 (1995). MSC: 55Q52 55T15 55P42 55P60 55Q40 PDFBibTeX XMLCite \textit{K. Shimomura}, Forum Math. 7, No. 6, 685--707 (1995; Zbl 0835.55009) Full Text: DOI EuDML
Shimomura, Katsumi; Yabe, Atsuko The homotopy groups \(\pi_ * (L_ 2 S^ 0)\). (English) Zbl 0832.55011 Topology 34, No. 2, 261-289 (1995). Reviewer: K.Knapp (Wuppertal) MSC: 55Q45 55T15 55P60 55P42 PDFBibTeX XMLCite \textit{K. Shimomura} and \textit{A. Yabe}, Topology 34, No. 2, 261--289 (1995; Zbl 0832.55011) Full Text: DOI
Inoue, Hiromi; Osakada, Yoshiko; Shimomura, Katsumi On some products of \(\beta\)-elements in the homotopy of the Moore spectrum. II. (English) Zbl 0862.55009 Math. J. Okayama Univ. 36, 185-197 (1994). Reviewer: S.O.Kochman (Downsview) MSC: 55Q45 55T15 PDFBibTeX XMLCite \textit{H. Inoue} et al., Math. J. Okayama Univ. 36, 185--197 (1994; Zbl 0862.55009)
Hikida, Mizuho; Shimomura, Katsumi An exact sequence related to Adams-Novikov \(E_ 2\)-terms of a cofibering. (English) Zbl 0817.55004 J. Math. Soc. Japan 46, No. 4, 645-661 (1994). Reviewer: M.Hikida (Hiroshima), K.Shimomura (Tottori) MSC: 55T15 55T25 55P42 PDFBibTeX XMLCite \textit{M. Hikida} and \textit{K. Shimomura}, J. Math. Soc. Japan 46, No. 4, 645--661 (1994; Zbl 0817.55004) Full Text: DOI
Shimomura, Katsumi; Yokotani, Masaaki Existence of the Greek letter elements in the stable homotopy groups of \(E(n)_ *\)-localized spheres. (English) Zbl 0824.55002 Publ. Res. Inst. Math. Sci. 30, No. 1, 139-150 (1994). Reviewer: J.Hodgson (Philadelphia) MSC: 55N22 55Q45 55T15 55N20 55P42 55Q10 57R77 PDFBibTeX XMLCite \textit{K. Shimomura} and \textit{M. Yokotani}, Publ. Res. Inst. Math. Sci. 30, No. 1, 139--150 (1994; Zbl 0824.55002) Full Text: DOI
Shimomura, Katsumi; Yabe, Atsuko On the chromatic \(E_ 1\)-term \(H^*M_ 0^ 2\). (English) Zbl 0810.55010 Friedlander, Eric M. (ed.) et al., Topology and representation theory. Conference on the connections between topology and representation theory held at Northwestern University, Evanston, IL (USA), May 1-5, 1992. Providence, RI: American Mathematical Society. Contemp. Math. 158, 217-228 (1994). Reviewer: J.McCleary (Poughkeepsie) MSC: 55T99 55T15 55N22 55Q45 PDFBibTeX XMLCite \textit{K. Shimomura} and \textit{A. Yabe}, Contemp. Math. 158, 217--228 (1994; Zbl 0810.55010)
Mahowald, Mark; Shimomura, Katsumi The Adams-Novikov spectral sequence for the \(L_ 2\) localization of a \(v_ 2\) spectrum. (English) Zbl 0791.55005 Tangora, Martin C. (ed.), Algebraic topology, Oaxtepec 1991. Proceedings of an international conference on algebraic topology, held July 4-11, 1991 in Oaxtepec, Mexico. Providence, RI: American Mathematical Society. Contemp. Math. 146, 237-250 (1993). Reviewer: D.Davis (Bethlehem) MSC: 55P42 55T15 PDFBibTeX XMLCite \textit{M. Mahowald} and \textit{K. Shimomura}, Contemp. Math. 146, 237--250 (1993; Zbl 0791.55005)
Mabuchi, Miho; Shimomura, Katsumi On some products of \(\beta\)-elements in the homotopy of the Moore spectrum. (English) Zbl 0861.55025 Math. J. Okayama Univ. 34, 195-204 (1992). Reviewer: Hal Sadofsky (MR 96a:55022) MSC: 55T15 55Q10 PDFBibTeX XMLCite \textit{M. Mabuchi} and \textit{K. Shimomura}, Math. J. Okayama Univ. 34, 195--204 (1992; Zbl 0861.55025)
Shimomura, Katsumi A spectrum whose \(BP_ *\)-homology is \((BP_ */{}I_ 5)[t_ 1]\). (English) Zbl 0757.55010 Hiroshima Math. J. 21, No. 3, 587-595 (1991). Reviewer: W.Singhof (Düsseldorf) MSC: 55P42 55N22 PDFBibTeX XMLCite \textit{K. Shimomura}, Hiroshima Math. J. 21, No. 3, 587--595 (1991; Zbl 0757.55010)
Shimomura, Katsumi On the products \(\beta_ s\beta_ t\) in the stable homotopy groups of spheres. (English) Zbl 0713.55008 Hiroshima Math. J. 19, No. 2, 347-354 (1989). Reviewer: Y.Furukawa MSC: 55Q45 55Q10 55T15 PDFBibTeX XMLCite \textit{K. Shimomura}, Hiroshima Math. J. 19, No. 2, 347--354 (1989; Zbl 0713.55008)
Shimomura, Katsumi Triviality of products of \(\beta\)-elements in the stable homotopy group of spheres. (English) Zbl 0698.55012 J. Math. Kyoto Univ. 29, No. 1, 57-67 (1989). Reviewer: S.Thomeier MSC: 55Q45 55P42 55P60 55Q40 PDFBibTeX XMLCite \textit{K. Shimomura}, J. Math. Kyoto Univ. 29, No. 1, 57--67 (1989; Zbl 0698.55012) Full Text: DOI
Shimomura, Katsumi Non-triviality of some products of \(\beta\)-elements in the stable homotopy of spheres. (English) Zbl 0642.55008 Hiroshima Math. J. 17, 349-353 (1987). Reviewer: Y.Furukawa MSC: 55Q45 PDFBibTeX XMLCite \textit{K. Shimomura}, Hiroshima Math. J. 17, 349--353 (1987; Zbl 0642.55008)
Shimomura, Katsumi; Yosimura, Zen-ichi BP-Hopf module spectrum and \(BP_ *\)-Adams spectral sequence. (English) Zbl 0636.55003 Publ. Res. Inst. Math. Sci. 22, 925-947 (1986). Reviewer: A.Liulevicius MSC: 55P42 55N20 55T25 PDFBibTeX XMLCite \textit{K. Shimomura} and \textit{Z.-i. Yosimura}, Publ. Res. Inst. Math. Sci. 22, 925--947 (1986; Zbl 0636.55003) Full Text: DOI
Shimomura, Katsumi; Tamura, Hidetaka Non-triviality of some compositions of \(\beta\)-elements in the stable homotopy of the Moore spaces. (English) Zbl 0606.55009 Hiroshima Math. J. 16, 121-133 (1986). Reviewer: D.W.Kahn MSC: 55P42 55T15 55Q10 PDFBibTeX XMLCite \textit{K. Shimomura} and \textit{H. Tamura}, Hiroshima Math. J. 16, 121--133 (1986; Zbl 0606.55009)
Shimomura, Katsumi On the Adams-Novikov spectral sequence and products of \(\beta\)-elements. (English) Zbl 0605.55013 Hiroshima Math. J. 16, 209-224 (1986). Reviewer: E.Ossa MSC: 55Q45 55T15 55T25 PDFBibTeX XMLCite \textit{K. Shimomura}, Hiroshima Math. J. 16, 209--224 (1986; Zbl 0605.55013)
Oka, Shichiro; Shimomura, Katsumi On products of the beta-elements in the stable homotopy of spheres. (English) Zbl 0515.55010 Hiroshima Math. J. 12, 611-626 (1982). MSC: 55Q45 55T15 PDFBibTeX XMLCite \textit{S. Oka} and \textit{K. Shimomura}, Hiroshima Math. J. 12, 611--626 (1982; Zbl 0515.55010)
Shimomura, Katsumi Novikov’s \(Ext^ 2\) at the prime 2. (English) Zbl 0485.55013 Hiroshima Math. J. 11, 499-513 (1981). MSC: 55T15 55N22 55Q45 PDFBibTeX XMLCite \textit{K. Shimomura}, Hiroshima Math. J. 11, 499--513 (1981; Zbl 0485.55013)