On the coefficient groups of equivariant -theory
Author:
Yimin Yang
Journal:
Trans. Amer. Math. Soc. 347 (1995), 77-98
MSC:
Primary 55N91; Secondary 19L47, 55N15, 57S15, 57S17
DOI:
https://doi.org/10.1090/S0002-9947-1995-1257645-1
MathSciNet review:
1257645
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Abstract: We calculated the coefficient groups of equivariant -theory for any cyclic group, and we proved that, for any compact Lie group, the coefficient groups can only have
-torsion. If there is any
-torsion, it is detected by
-primary finite subgroups of
. The rationalization of the coefficient groups then can be easily calculated.
- [1] W. Burnside, Theory of groups of finite order, Cambridge Univ. Press, 1911.
- [2]
Stefan Jackowski, Equivariant
-theory and cyclic subgroups, London Math. Soc. Lecture Notes Ser., vol. 26, Cambridge Univ. Press, 1977, pp. 76-91. MR 0448377 (56:6684)
- [3]
G. Lewis, J. P. May, and J. E. McClure, Ordinary
-graded cohomology, Bull. Amer. Math. Soc. (N.S.) 4 (1981), 208-212. MR 598689 (82e:55008)
- [4] G. Lewis, Jr., J. P. May, and M. Steinberg (with contributions by J. E. McClure), Equivariant stable homotopy theory, Lecture Notes in Math., vol. 1213, Springer-Verlag, 1986. MR 866482 (88e:55002)
- [5]
James E. McClure, Restriction maps in equivariant
-theory, Topology 25 (1986), 399-409. MR 862427 (88f:55022)
- [6]
Ryszard L. Rubinsztein, Restriction of equivariant
-theory, Bull. Acad. Polon. Sci. Sér. Sci. Math. 29 (1981, no. 5-6). MR 640476 (83a:55008)
- [7]
G. B. Segal, Equivariant
-theory, Publ. Math. Inst. Hautes Étude Sci. 34 (1968), 129-151.
- [8] J.-P. Serre, Linear representations of finite groups, Springer-Verlag, 1977. MR 0450380 (56:8675)
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1995-1257645-1
Article copyright:
© Copyright 1995
American Mathematical Society