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Borsuk-Ulam type theorems for compact Lie group actions

Authors: Yasuhiro Hara and Norihiko Minami
Journal: Proc. Amer. Math. Soc. 132 (2004), 903-909
MSC (2000): Primary 58E40, 55R12, 55N20; Secondary 55R35
Published electronically: August 28, 2003
MathSciNet review: 2019972
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Abstract: Borsuk-Ulam type theorems for arbitrary compact Lie group actions are proven. The transfer plays a major role in this approach.

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  • [ASe69] M. F. Atiyah and G. B. Segal, Equivariant $K$-theory and completion, J. Differential Geometry 3 (1969), 1-18. MR 41:4575
  • [ASi71] M. F. Atiyah and I. M. Singer, The index of elliptic operators: IV, Ann. of Math. 93 (1971), 119-138. MR 43:5554
  • [BG75] J. C. Becker and D. H. Gottlieb, The transfer map and fiber bundles, Topology 14 (1975), 1-12. MR 51:14042
  • [Boa66] J. M. Boardman, Stable Homotopy Theory (mimeographed), University of Warwick, 1966.
  • [Dol76] A. Dold, The fixed point transfer of fibre-preserving maps, Math. Z. 148 (1976), 215-244. MR 55:6416
  • [FH88] E. Fadell and S. Husseini, An ideal-valued cohomological index theory with applications to Borsuk-Ulam and Bourgin-Yang theorems, Ergodic Theory Dynam. Systems 8 (1988), 73-85. MR 89k:55002
  • [KP72] D. S. Kahn and S. B. Priddy, Applications of the transfer to stable homotopy theory, Bull. Amer. Math. Soc. 78 (1972), 981-987. MR 46:8220
  • [Kaw91] K. Kawakubo, The Theory of Transformation Groups, The Clarendon Press, Oxford University Press, 1991. MR 93g:57044
  • [Kob86] T. Kobayashi, The Borsuk-Ulam theorem for a $Z_q$-map from a $\mathbb{Z} _q$-space to $S^{2n+1}$, Proc. Amer. Math. Soc. 97 (1986), 714-716. MR 87g:55001
  • [LMS86] L. G. Lewis, J. P. May, and M. Steinberger, Equivariant Stable Homotopy Theory, Lecture Notes in Math. No. 1213, Springer-Verlag, Berlin, Heidelberg, New York, 1986. MR 88e:55002
  • [Mos57] G. D. Mostow, Equivariant embeddings in Euclidean space, Ann. Math. 65 (1957), 432-446. MR 19:291c
  • [Rou71] F. W. Roush, Transfer in generalized cohomology theories, Ph.D. thesis, Princeton University, 1971.

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Additional Information

Yasuhiro Hara
Affiliation: Department of Mathematics, Graduate School of Science, Osaka University, Osaka, Japan

Norihiko Minami
Affiliation: Department of Mathematics, Nagoya Institute of Technology, Gokiso, Showa-ku, Nagoya 466-8555, Japan

Keywords: Borsuk-Ulam type theorems, transfer, generalized cohomology theories
Received by editor(s): March 22, 2002
Received by editor(s) in revised form: August 12, 2002, and October 25, 2002
Published electronically: August 28, 2003
Additional Notes: The second author was partially supported by Grant-in-Aid for Scientific Research No. 13440020, Japan Society for the Promotion of Science
Communicated by: Paul Goerss
Article copyright: © Copyright 2003 American Mathematical Society

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