Induction theorems for equivariant K-theory and J-theory

Katsuo KAWAKUBO

doi:10.2969/jmsj/03820173

Katsuo KAWAKUBO

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JOURNAL FREE ACCESS

1986 Volume 38 Issue 2 Pages 173-198

DOI https://doi.org/10.2969/jmsj/03820173

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Published: 1986 Received: May 04, 1984 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: SUBTITLE Details: Wrong : Dedicated to Professor Nobuo Shimada on his sixtieth birthday

Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) M. F. Atiyah and G. B. Segal, Equivariant K-theory, (mimeographed note), University of Warwick.
2) M. F. Atiyah and I. M. Singer, The index of elliptic operators III, Ann. of Math., 87 (1968), 546-604.
3) H. Bass, Algebraic K-theory, Benjamin, New York, 1968.
4) A. W. M. Dress, Notes on the theory of representations of a finite group, I: The Burnside ring of a finite group and some AGN applications, (multicopied notes), Bielefeld, 1971.
5) Z. Fiedorowicz, H. Hauschild and J. P. May, Equivariant algebraic K-theory, Proceedings of the Oberwolfach Conference on Algebraic K-theory.
6) J. A. Green, Axiomatic representation theory for finite groups, J. Pure Appl. Alg., 1 (1971), 41-77.
7) S. Jackowski, Equivariant K-theory and cyclic subgroups, London Math. Soc. Lecture Note Series, 26 (1977), Cambridge Univ. Press, 76-91.
8) K. Kawakubo, G-homotopy equivalent manifolds and J_G-homomorphism, Proc. Japan Acad., 54 (1978), 104-106.
9) K. Kawakubo, Compact Lie group actions and fiber homotopy type, J. Math. Soc. Japan, 33 (1981), 295-321.
10) K. Kawakubo, G-vector bundles and F-projective modules, Proc. Japan Acad., 59 (1983), 248-251.
11) K. Kawakubo, Representations over G-rings and cohomology, Proc. Japan Acad., 60(1984), 66-69.
12) T. Y. Lam, Induction theorems for Grothendieck groups and Whitehead groups of finite groups, Ann. Sci. École Norm. Sup. 4è séries, 1 (1968), 91-148.
13) J. E. McClure, On the groups JO_G (X) I, Math. Z., 183 (1983), 229-253.
14) J. Milnor, Introduction to algebraic K-theory, Ann. of Math. Studies, 72 (1971).
15) T. Petrie, Smith equivalence of representations, preprint, 1982.
16) T. Petrie and J. Randall, Transformation groups on manifolds, Decker Lecture Series, 1983.
17) D. Quillen, Higher algebraic K-theory I, Lecture Notes in Math., 341 (1973), Springer, 85-147.
18) J. P. Serre, Cohomologie Galoisienne, Lecture Notes in Math., 5 (1964), Springer.
19) J. P. Serre, Représentations linéaires des groupes finis, Hermann, Paris, 1971.
20) R. G. Swan, Induced representations and projective modules, Ann. of Math., 71 (1960), 552-578.
21) R. G. Swan, Vector bundles and projective modules, Trans. Amer. Math. Soc., 105 (1962), 264-277.
22) T. Yoshida, Transfer theory in topos, (in Japanese) Sugaku, 32 (1980), 193-212.
23) M. F. Atiyah, Characters and cohomology of finite groups, Publ. Math. I. H. E. S., 9 (1961), 23-64.
24) H. Fukagawa, Equivariant transfer for finite G-coverings, Japan. J. Math., 10 (1984), 117-135.
25) G. Nishida, The transfer homomorphism in equivariant generalized cohomology theories, J. Math. Kyoto Univ., 18 (1978), 435-451.

Right : [1] M. F. Atiyah and G. B. Segal, Equivariant K-theory, (mimeographed note), University of Warwick.
[2] M. F. Atiyah and I. M. Singer, The index of elliptic operators III, Ann. of Math., 87 (1968), 546-604.
[3] H. Bass, Algebraic K-theory, Benjamin, New York, 1968.
[4] A. W. M. Dress, Notes on the theory of representations of a finite group, I: The Burnside ring of a finite group and some AGN applications, (multicopied notes), Bielefeld, 1971.
[5] Z. Fiedorowicz, H. Hauschild and J. P. May, Equivariant algebraic K-theory, Proceedings of the Oberwolfach Conference on Algebraic K-theory.
[6] J. A. Green, Axiomatic representation theory for finite groups, J. Pure Appl. Alg., 1 (1971), 41-77.
[7] S. Jackowski, Equivariant K-theory and cyclic subgroups, London Math. Soc. Lecture Note Series, 26 (1977), Cambridge Univ. Press, 76-91.
[8] K. Kawakubo, G-homotopy equivalent manifolds and J_G-homomorphism, Proc. Japan Acad., 54 (1978), 104-106.
[9] K. Kawakubo, Compact Lie group actions and fiber homotopy type, J. Math. Soc. Japan, 33 (1981), 295-321.
[10] K. Kawakubo, G-vector bundles and F-projective modules, Proc. Japan Acad., 59 (1983), 248-251.
[11] K. Kawakubo, Representations over G-rings and cohomology, Proc. Japan Acad., 60 (1984), 66-69.
[12] T. Y. Lam, Induction theorems for Grothendieck groups and Whitehead groups of finite groups, Ann. Sci. École Norm. Sup. 4è séries, 1 (1968), 91-148.
[13] J. E. McClure, On the groups JO_G(X) I, Math. Z., 183 (1983), 229-253.
[14] J. Milnor, Introduction to algebraic K-theory, Ann. of Math. Studies, 72 (1971).
[15] T. Petrie, Smith equivalence of representations, preprint, 1982.
[16] T. Petrie and J. Randall, Transformation groups on manifolds, Decker Lecture Series, 1983.
[17] D. Quillen, Higher algebraic K-theory I, Lecture Notes in Math., 341 (1973), Springer, 85-147.
[18] J. P. Serre, Cohomologie Galoisienne, Lecture Notes in Math., 5 (1964), Springer.
[19] J. P. Serre, Représentations linéaires des groupes finis, Hermann, Paris, 1971.
[20] R. G. Swan, Induced representations and projective modules, Ann. of Math., 71 (1960), 552-578.
[21] R. G. Swan, Vector bundles and projective modules, Trans. Amer. Math. Soc., 105 (1962), 264-277.
[22] T. Yoshida, Transfer theory in topos, (in Japanese) Sugaku, 32 (1980), 193-212.
[23] M. F. Atiyah, Characters and cohomology of finite groups, Publ. Math. I. H. E. S., 9 (1961), 23-64.
[24] H. Fukagawa, Equivariant transfer for finite G-coverings, Japan. J. Math., 10 (1984), 117-135.
[25] G. Nishida, The transfer homomorphism in equivariant generalized cohomology theories, J. Math. Kyoto Univ., 18 (1978), 435-451.

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