Crabb, M. C. Fibrewise topological complexity of sphere and projective bundles. arXiv:2305.12836 Preprint, arXiv:2305.12836 [math.AT] (2023). MSC: 55M30 55R25 55S40 55P42 55R40 55R70 BibTeX Cite \textit{M. C. Crabb}, ``Fibrewise topological complexity of sphere and projective bundles'', Preprint, arXiv:2305.12836 [math.AT] (2023) Full Text: arXiv OA License
Crabb, M. C. Equivariant maps between spheres: Nagasaki’s examples. (English) Zbl 1507.55002 J. Fixed Point Theory Appl. 24, No. 4, Paper No. 78, 8 p. (2022). Reviewer: João Peres Vieira (Rio Claro) MSC: 55M20 55P91 55Q91 PDFBibTeX XMLCite \textit{M. C. Crabb}, J. Fixed Point Theory Appl. 24, No. 4, Paper No. 78, 8 p. (2022; Zbl 1507.55002) Full Text: DOI
Crabb, M. C. Nielsen-Reidemeister indices for multivalued maps. (English) Zbl 1392.55004 Bull. Belg. Math. Soc. - Simon Stevin 24, No. 4, 483-499 (2017). Reviewer: Valerii V. Obukhovskij (Voronezh) MSC: 55M20 54H25 55P42 55R70 PDFBibTeX XMLCite \textit{M. C. Crabb}, Bull. Belg. Math. Soc. - Simon Stevin 24, No. 4, 483--499 (2017; Zbl 1392.55004) Full Text: Euclid
Crabb, Michael; Ranicki, Andrew The geometric Hopf invariant and surgery theory. (English) Zbl 1404.55001 Springer Monographs in Mathematics. Cham: Springer (ISBN 978-3-319-71305-2/hbk; 978-3-319-71306-9/ebook). xvi, 397 p. (2017). Reviewer: Jonathan Hodgson (Swarthmore) MSC: 55-02 55Q10 55Q25 57R65 57R67 PDFBibTeX XMLCite \textit{M. Crabb} and \textit{A. Ranicki}, The geometric Hopf invariant and surgery theory. Cham: Springer (2017; Zbl 1404.55001) Full Text: DOI arXiv
Crabb, M. C. Lefschetz indices for \(n\)-valued maps. (English) Zbl 1329.55001 J. Fixed Point Theory Appl. 17, No. 1, 153-186 (2015). Reviewer: Daciberg Lima Gonçalves (São Paulo) MSC: 55M20 54H25 55P42 55P91 55R70 57M10 PDFBibTeX XMLCite \textit{M. C. Crabb}, J. Fixed Point Theory Appl. 17, No. 1, 153--186 (2015; Zbl 1329.55001) Full Text: DOI
Crabb, M. C. Fixed-orbit indices. I. (English) Zbl 1258.55001 J. Fixed Point Theory Appl. 11, No. 1, 65-92 (2012). Reviewer: Christian Fenske (Gießen) MSC: 55M20 54H25 55P42 55P91 55R70 55R91 PDFBibTeX XMLCite \textit{M. C. Crabb}, J. Fixed Point Theory Appl. 11, No. 1, 65--92 (2012; Zbl 1258.55001) Full Text: DOI
Crabb, M. C. Spaces of commuting elements in SU(2). (English) Zbl 1222.55007 Proc. Edinb. Math. Soc., II. Ser. 54, No. 1, 67-75 (2011). Reviewer: Markus Szymik (Bochum) MSC: 55P42 55P91 PDFBibTeX XMLCite \textit{M. C. Crabb}, Proc. Edinb. Math. Soc., II. Ser. 54, No. 1, 67--75 (2011; Zbl 1222.55007) Full Text: DOI
Crabb, M. C. The homotopy coincidence index. (English) Zbl 1205.55002 J. Fixed Point Theory Appl. 7, No. 1, 1-32 (2010). MSC: 55M20 55S35 55R70 54H25 55P42 57R19 PDFBibTeX XMLCite \textit{M. C. Crabb}, J. Fixed Point Theory Appl. 7, No. 1, 1--32 (2010; Zbl 1205.55002) Full Text: DOI
Crabb, M. C. A fibrewise stable splitting and free loops on projective spaces. (English) Zbl 1211.55005 Félix, Yves (ed.) et al., Homotopy theory of function spaces and related topics. Proceedings of the Oberwolfach workshop, Mathematisches Forschungsinstitut Oberwolfach, Germany, April 5–11, 2009. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4929-3/pbk). Contemporary Mathematics 519, 67-75 (2010). Reviewer: Kohhei Yamaguchi (Tokyo) MSC: 55P35 55P91 55P40 55R70 PDFBibTeX XMLCite \textit{M. C. Crabb}, Contemp. Math. 519, 67--75 (2010; Zbl 1211.55005)
Crabb, M. C.; Jaworowski, J. Theorems of Kakutani and Dyson revisited. (English) Zbl 1214.55002 J. Fixed Point Theory Appl. 5, No. 2, 227-236 (2009). Reviewer: Christian Fenske (Gießen) (MR2741182) MSC: 55M20 55P42 55N15 PDFBibTeX XMLCite \textit{M. C. Crabb} and \textit{J. Jaworowski}, J. Fixed Point Theory Appl. 5, No. 2, 227--236 (2009; Zbl 1214.55002) Full Text: DOI
Crabb, M. C. Equivariant fixed-point indices of iterated maps. (English) Zbl 1142.37020 J. Fixed Point Theory Appl. 2, No. 2, 171-193 (2007). MSC: 37C25 55M20 55N91 55P91 37B30 PDFBibTeX XMLCite \textit{M. C. Crabb}, J. Fixed Point Theory Appl. 2, No. 2, 171--193 (2007; Zbl 1142.37020) Full Text: DOI
Crabb, M. C. Brauer induction and equivariant stable homotopy. (English) Zbl 0991.20004 Arch. Math. 77, No. 6, 469-475 (2001). Reviewer: Victor P.Snaith (Southampton) MSC: 20C15 55P91 19A22 PDFBibTeX XMLCite \textit{M. C. Crabb}, Arch. Math. 77, No. 6, 469--475 (2001; Zbl 0991.20004) Full Text: DOI
Bauer, S.; Crabb, M. C.; Spreafico, M. The classifying space of the gauge group of an \(SO(3)\)-bundle over \(S^2\). (English) Zbl 0997.55019 Proc. R. Soc. Edinb., Sect. A, Math. 131, No. 4, 767-783 (2001). Reviewer: G.Peschke (Edmonton) MSC: 55R35 55P42 55R40 55P35 PDFBibTeX XMLCite \textit{S. Bauer} et al., Proc. R. Soc. Edinb., Sect. A, Math. 131, No. 4, 767--783 (2001; Zbl 0997.55019) Full Text: DOI
Bauer, Sven; Crabb, Michael; Spreafico, Mauro The space of free loops on a real projective space. (English) Zbl 0980.55006 Maruyama, Ken-ichi (ed.) et al., Groups of homotopy self-equivalences and related topics. Proceedings of the workshop, Gargnano, Italy, September 5-11, 1999. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 274, 33-38 (2001). Reviewer: Kohhei Yamaguchi (Tokyo) MSC: 55P35 57R70 55P91 55P42 58E05 PDFBibTeX XMLCite \textit{S. Bauer} et al., Contemp. Math. 274, 33--38 (2001; Zbl 0980.55006)
Crabb, M. C.; Sutherland, W. A. Counting homotopy types of gauge groups. (English) Zbl 1024.55005 Proc. Lond. Math. Soc., III. Ser. 81, No. 3, 747-768 (2000). Reviewer: W.A.Sutherland MSC: 55P15 55R10 PDFBibTeX XMLCite \textit{M. C. Crabb} and \textit{W. A. Sutherland}, Proc. Lond. Math. Soc. (3) 81, No. 3, 747--768 (2000; Zbl 1024.55005) Full Text: DOI
Crabb, M. C.; Sutherland, W. A.; Zhang, Ping Homotopy nilpotency. (English) Zbl 0932.55007 Q. J. Math., Oxf. II. Ser. 50, No. 198, 179-196 (1999). Reviewer: M.Golasiński (Toruń) MSC: 55P45 55R70 PDFBibTeX XMLCite \textit{M. C. Crabb} et al., Q. J. Math., Oxf. II. Ser. 50, No. 198, 179--196 (1999; Zbl 0932.55007) Full Text: DOI
Crabb, Michael; James, Ioan Fibrewise homotopy theory. (English) Zbl 0905.55001 Springer Monographs in Mathematics. London: Springer. viii, 341 p. (1998). Reviewer: S.Papadima (Bucureşti) MSC: 55-02 55R65 55P42 55P99 55R99 PDFBibTeX XMLCite \textit{M. Crabb} and \textit{I. James}, Fibrewise homotopy theory. London: Springer (1998; Zbl 0905.55001)
Crabb, M. C.; Xu, Kai Quadratic spaces. (English) Zbl 0943.55004 Math. Z. 226, No. 2, 169-180 (1997). MSC: 55P42 57R19 55P60 11T99 57R15 11E88 PDFBibTeX XMLCite \textit{M. C. Crabb} and \textit{K. Xu}, Math. Z. 226, No. 2, 169--180 (1997; Zbl 0943.55004) Full Text: DOI
Crabb, M. C.; Hubbuck, J. R.; McCall, J. A. W. Stable summands of \(U(n)\). (English) Zbl 0883.55013 Proc. R. Soc. Edinb., Sect. A 127, No. 5, 963-973 (1997). MSC: 55Q10 55P42 55Q52 55Q20 57T20 PDFBibTeX XMLCite \textit{M. C. Crabb} et al., Proc. R. Soc. Edinb., Sect. A, Math. 127, No. 5, 963--973 (1997; Zbl 0883.55013) Full Text: DOI
Crabb, M. C.; Knapp, K. Applications of nonconnective \(Im(J)\)-theory. (English) Zbl 0864.55006 James, I. M. (ed.), Handbook of algebraic topology. Amsterdam: North-Holland. 463-503 (1995). Reviewer: C.Costinescu (Bucureşti) MSC: 55P42 PDFBibTeX XMLCite \textit{M. C. Crabb} and \textit{K. Knapp}, in: Handbook of algebraic topology. Amsterdam: North-Holland. 463--503 (1995; Zbl 0864.55006)
Crabb, M. C.; Sutherland, W. A. How non-abelian is non-abelian gauge theory? (English) Zbl 0863.55006 Q. J. Math., Oxf. II. Ser. 46, No. 183, 279-290 (1995). Reviewer: J.Jaworowski (Bloomington) MSC: 55P45 57R22 PDFBibTeX XMLCite \textit{M. C. Crabb} and \textit{W. A. Sutherland}, Q. J. Math., Oxf. II. Ser. 46, No. 183, 279--290 (1995; Zbl 0863.55006) Full Text: DOI
Crabb, M. C.; James, I. M. Fibrewise configuration spaces. (English) Zbl 0849.55012 Bol. Soc. Mat. Mex., II. Ser. 37, No. 1-2, 83-97 (1992). Reviewer: S.Papadima (Bucureşti) MSC: 55P99 57R40 PDFBibTeX XMLCite \textit{M. C. Crabb} and \textit{I. M. James}, Bol. Soc. Mat. Mex., II. Ser. 37, No. 1--2, 83--97 (1992; Zbl 0849.55012)
Crabb, M. C.; Hubbuck, J. R.; Xu, Kai Fields of spaces. (English) Zbl 0758.55003 Adams memorial symposium on algebraic topology, vol. 1, Proc. Symp., Manchester/UK 1990, Lond. Math. Soc. Lect. Note Ser. 175, 241-254 (1992). Reviewer: J.W.Rutter (Liverpool) MSC: 55P15 55P10 55P42 55P45 16N20 20D25 PDFBibTeX XMLCite \textit{M. C. Crabb} et al., Lond. Math. Soc. Lect. Note Ser. 175, 241--254 (1992; Zbl 0758.55003)
Crabb, M. C. On the \(KO_{{\mathbb{Z}}/2}\)-Euler class. II. (English) Zbl 0723.55011 Proc. R. Soc. Edinb., Sect. A 117, No. 1-2, 139-154 (1991). Reviewer: C.Costinescu (Bucureşti) MSC: 55S91 55N91 PDFBibTeX XMLCite \textit{M. C. Crabb}, Proc. R. Soc. Edinb., Sect. A, Math. 117, No. 1--2, 139--154 (1991; Zbl 0723.55011) Full Text: DOI
Crabb, M. C. The Fuller index and \(\mathbb{T}\)-equivariant stable homotopy theory. (English) Zbl 0735.58007 Théorie de l’homotopie, Colloq. CNRS-NSF-SMF, Luminy/Fr. 1988, Astérisque 191, 71-86 (1990). Reviewer: K.Furutani (Chiba-ken) MSC: 58C30 37G99 55P91 PDFBibTeX XMLCite \textit{M. C. Crabb}, Astérisque 191, 71--86 (1990; Zbl 0735.58007)
Crabb, M. C. Invariants of fixed-point-free circle actions. (English) Zbl 0696.55011 Advances in homotopy theory, Proc. Conf. in Honour of I. M. James, Cortona/Italy 1988, Lond. Math. Soc. Lect. Note Ser. 139, 21-44 (1989). Reviewer: K.Knapp MSC: 55P42 55N15 57S15 PDFBibTeX XML
Crabb, M. C. Periodicity in \({\mathbb{Z}}/4\)-equivariant stable homotopy theory. (English) Zbl 0696.55006 Algebraic topology, Proc. Int. Conf., Evanston/IL 1988, Contemp. Math. 96, 109-124 (1989). Reviewer: K.Knapp MSC: 55N15 55P42 57S17 PDFBibTeX XML
Crabb, M. C.; Gonçalves, D. L. On the space of matrices of given rank. (English) Zbl 0678.55003 Proc. Edinb. Math. Soc., II. Ser. 32, No. 1, 99-105 (1989). Reviewer: F.Gomez MSC: 55P42 55R10 PDFBibTeX XMLCite \textit{M. C. Crabb} and \textit{D. L. Gonçalves}, Proc. Edinb. Math. Soc., II. Ser. 32, No. 1, 99--105 (1989; Zbl 0678.55003) Full Text: DOI
Crabb, M. C.; Mitchell, S. A. The loops on U(n)/O(n) and U(2n)/Sp(n). (English) Zbl 0667.55006 Math. Proc. Camb. Philos. Soc. 104, No. 1, 95-103 (1988). Reviewer: M.Mimura MSC: 55P35 57T25 55P42 PDFBibTeX XMLCite \textit{M. C. Crabb} and \textit{S. A. Mitchell}, Math. Proc. Camb. Philos. Soc. 104, No. 1, 95--103 (1988; Zbl 0667.55006) Full Text: DOI
Crabb, M. C.; Knapp, K. The Hurewicz map on stunted complex projective spaces. (English) Zbl 0665.55007 Am. J. Math. 110, No. 5, 783-809 (1988). Reviewer: Y.Furukawa MSC: 55Q10 55Q50 55N15 55P42 55R50 PDFBibTeX XMLCite \textit{M. C. Crabb} and \textit{K. Knapp}, Am. J. Math. 110, No. 5, 783--809 (1988; Zbl 0665.55007) Full Text: DOI
Crabb, Michael; Knapp, Karlheinz Central Adams operators. (English) Zbl 0638.55005 Manuscr. Math. 60, No. 2, 131-137 (1988). Reviewer: M.Mimura MSC: 55N15 55P42 55R50 55Q10 PDFBibTeX XMLCite \textit{M. Crabb} and \textit{K. Knapp}, Manuscr. Math. 60, No. 2, 131--137 (1988; Zbl 0638.55005) Full Text: DOI EuDML
Crabb, M. C.; Knapp, K. James numbers. (English) Zbl 0627.57026 Math. Ann. 282, No. 3, 395-422 (1988). MSC: 57T20 55Q52 55Q10 PDFBibTeX XMLCite \textit{M. C. Crabb} and \textit{K. Knapp}, Math. Ann. 282, No. 3, 395--422 (1988; Zbl 0627.57026) Full Text: DOI EuDML
Crabb, M. C.; Knapp, K. Snaith periodicity. (English) Zbl 0657.55009 Q. J. Math., Oxf. II. Ser. 38, 307-312 (1987). Reviewer: S.Thomeier MSC: 55P42 55Q10 55Q50 55R50 PDFBibTeX XMLCite \textit{M. C. Crabb} and \textit{K. Knapp}, Q. J. Math., Oxf. II. Ser. 38, 307--312 (1987; Zbl 0657.55009) Full Text: DOI
Crabb, M. C. On the stable splitting of U(n) and \(\Omega\) U(n). (English) Zbl 0647.55008 Algebraic topology, Proc. Symp., Barcelona/Spain 1986, Lect. Notes Math. 1298, 35-53 (1987). Reviewer: V.P.Snaith MSC: 55P42 55R35 55P35 PDFBibTeX XML
Crabb, M. C.; Knapp, K. H.; Morisugi, K. On the stable Hurewicz image of stunted quaternionic projective spaces. (English) Zbl 0638.55011 Homotopy theory and related topics, Pap. Symp. Kyoto/Jap. 1984, Adv. Stud. Pure Math. 9, 319-334 (1987). Reviewer: P.Landweber MSC: 55Q10 55R50 55N15 PDFBibTeX XML
Crabb, M. C.; Knapp, K. James quasi-periodicity for the codegree of vector bundles over complex projective spaces. (English) Zbl 0627.55013 J. Lond. Math. Soc., II. Ser. 35, 353-366 (1987). Reviewer: S.O.Kochman MSC: 55R50 55R25 55Q10 57T20 PDFBibTeX XMLCite \textit{M. C. Crabb} and \textit{K. Knapp}, J. Lond. Math. Soc., II. Ser. 35, 353--366 (1987; Zbl 0627.55013) Full Text: DOI
Crabb, M. C.; Sutherland, W. A. The space of sections of a sphere-bundle. I. (English) Zbl 0614.55012 Proc. Edinb. Math. Soc., II. Ser. 29, 383-403 (1986). Reviewer: V.L.Hansen MSC: 55R99 55S40 58D15 PDFBibTeX XMLCite \textit{M. C. Crabb} and \textit{W. A. Sutherland}, Proc. Edinb. Math. Soc., II. Ser. 29, 383--403 (1986; Zbl 0614.55012) Full Text: DOI
Crabb, M. C.; Knapp, K. Adams periodicity in stable homotopy. (English) Zbl 0581.55008 Topology 24, 475-486 (1985). Reviewer: M.Mimura MSC: 55Q10 55S25 55P42 55R50 55Q50 PDFBibTeX XMLCite \textit{M. C. Crabb} and \textit{K. Knapp}, Topology 24, 475--486 (1985; Zbl 0581.55008) Full Text: DOI
Crabb, M. C.; Sutherland, W. A. Function spaces and Hurwitz-Radon numbers. (English) Zbl 0581.55004 Math. Scand. 55, 67-90 (1984). Reviewer: V.L.Hansen MSC: 55P15 58D15 PDFBibTeX XMLCite \textit{M. C. Crabb} and \textit{W. A. Sutherland}, Math. Scand. 55, 67--90 (1984; Zbl 0581.55004) Full Text: DOI EuDML
Crabb, M. C. \(\mathbb{Z}/2\) - homotopy theory. (English) Zbl 0443.55001 London Mathematical Society Lecture Note Series, 44. Cambridge etc.: Cambridge University Press. 130 p. £6.95 (1980). MSC: 55-02 55P99 57R85 55Q35 55N15 55Q50 18F25 57S17 PDFBibTeX XML
Crabb, M. C.; Sutherland, W. A. A bundle over the tangent sphere-bundle of a \(\pi\)-manifold. (English) Zbl 0404.57023 Q. J. Math., Oxf. II. Ser. 30, 1-19 (1979). MSC: 57R25 55S35 55S40 13C10 PDFBibTeX XMLCite \textit{M. C. Crabb} and \textit{W. A. Sutherland}, Q. J. Math., Oxf. II. Ser. 30, 1--19 (1979; Zbl 0404.57023) Full Text: DOI