Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-26T20:20:14.405Z Has data issue: false hasContentIssue false

Group homomorphisms inducing an isomorphism of a functor

Dedicated to Professor Nobuo Shimada on his 60th birthday

Published online by Cambridge University Press:  24 October 2008

Norihiko Minami
Affiliation:
Department of Mathematics, Northwestern University, Evanston IL 60201, U.S.A.and Department of Mathematics, Hiroshima University, Hiroshima 730; Japan

Extract

Whenever a covariant (resp. contravariant) functor F from a category of groups is given, it is natural to ask the following question: if a homomorphismof groups induces the isomorphism (resp., ), is f itself an isomorphism?

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1988

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Atiyah, M. F.. Characters and cohomology of finite groups. Inst. Hautes Études Sci. Publ. Math. 9 (1961), 2364.CrossRefGoogle Scholar
[2]Atiyah, M. F. and Segal, G. B.. Equivariant K-theory and completion. J. Differential Geom. 3 (1969), 118.CrossRefGoogle Scholar
[3]Bojanowska, A.. The spectrum of equivariant K-theory. Math. Z. 183 (1983), 119.CrossRefGoogle Scholar
[4]Borel, A.. Sur la cohomologie des espaces fibrés principaux et des espaces homogènes de groupes de Lie compacts. Ann. of Math. 57 (1953), 115207.CrossRefGoogle Scholar
[5]Buhštaber, V. M. and Miščcenko, A. S., A K-theory on the category of infinite cell complexes. Izv. Akad. Nauk Armyn SSR Ser. Mat. 32 (1968), 560604.Google Scholar
[6]Bourbaki, N.. Algèbre Commutative, chapters 5–6 (Hermann, 1964).Google Scholar
[7]Evens, L.. A generalization of the transfer map in the cohomology of groups. Trans. Amer. Math. Soc. 108 (1963), 5465.CrossRefGoogle Scholar
[8]Evens, L. and Kahn, D.. An integral Riemann–Roch formula for induced representations of finite groups. Trans. Amer. Math. Soc. 245 (1978), 331347.CrossRefGoogle Scholar
[9]Feshbach, M.. The Segal conjecture for compact Lie groups. Topology 26 (1987), 120.CrossRefGoogle Scholar
[10]Hilton, P. J. and Stambach, U.. A Course in Homological Algebra (Springer-Verlag, 1971).CrossRefGoogle Scholar
[11]Jackowski, S.. Group homomorphism inducing isomorphism of cohomology. Topology 17 (1978), 303307.CrossRefGoogle Scholar
[12]Matumoto, T., Minami, N. and Sugawara, M.. On the set of free homotopy classes and Brown's construction. Hiroshima Math. J. 14 (1984), 359369.CrossRefGoogle Scholar
[13]Minami, N.. On the I(G)-adic topology of the Burnside rings of compact Lie groups. Publ. Res. Inst. Math. Sci. 20 (1984), 447460.CrossRefGoogle Scholar
[14]Minami, N.. (In preparation).Google Scholar
[15]Nakaoka, M.. Decomposition theorem for homology of symmetric groups. Ann. of Math. 71 (1960), 1642.CrossRefGoogle Scholar
[16]Nishida, G.. On the S 1-Segal conjecture. Publ. Res. Inst. Math. Sci. 19 (1983), 11531162.CrossRefGoogle Scholar
[17]Segal, G.. The representation ring of a compact Lie group. Inst. Hautes Études Sci. Publ. Math. 34 (1968), 129151.CrossRefGoogle Scholar
[18]Suzuki, M.Group Theory II (Springer-Verlag, 1986).CrossRefGoogle Scholar
[19]Yoshimura, Z.. Universal coefficient sequences for cohomology theories of CW-spectra. Osaka J.Math. 12 (1975), 305323.Google Scholar
[20]Zeeman, E. C.. A proof of the comparison theorem for spectral sequences. Proc. Cambridge Philos. Soc. 53 (1957), 5762.CrossRefGoogle Scholar