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
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
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
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; 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)
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)
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)
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)
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)
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)
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)
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
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)
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)
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; 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)