Finite cyclic subgroups determine the spectrum of the equivariant -theory

Author:
Agnieszka Bojanowska

Journal:
Proc. Amer. Math. Soc. **113** (1991), 245-249

MSC:
Primary 55N91; Secondary 19M05, 22E99, 55N15

DOI:
https://doi.org/10.1090/S0002-9939-1991-1064899-5

MathSciNet review:
1064899

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Equivariant maps inducing an equivalence of the categories of components of the fixed point sets of topologically cyclic subgroups are considered. It is shown that they are the same as those inducing an equivalence of the categories of components of the fixed point sets of finite cyclic subgroups. It follows that equivariant maps inducing a bijection of maximal ideals of the appropriate equivariant -theory rings coincide with those which give bijection on the sets of all prime ideals. As a corollary we obtain that a group homomorphism inducing bijection of maximal ideals of the representation rings is an isomorphism.

**[B]**A. Bojanowska,*The spectrum of equivariant**-theory*, Math. Z.**183**(1983), 1-19. MR**701356 (85a:55003)****[tD]**T. Tom Dieck,*Transformation groups and representation theory*, Lecture Notes in Math., vol. 766, Springer-Verlag, Berlin, Heidelberg, and New York, 1979. MR**551743 (82c:57025)****[M]**N. Minami,*Group homomorphisms inducing an isomorphism of a functor*, Math. Proc. Cambridge Philos. Soc.**104**(1990), 81-93. MR**938453 (89h:55007)****[Mc]**J. McClure,*Restriction maps in equivariant**-theory*, Topology**25**(1986), 399-411. MR**862427 (88f:55022)****[Q]**D. Quillen,*The spectrum of equivariant cohomology ring*I, II, Ann. of Math.**94**(1971), 549-602. MR**0298694 (45:7743)**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
55N91,
19M05,
22E99,
55N15

Retrieve articles in all journals with MSC: 55N91, 19M05, 22E99, 55N15

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1991-1064899-5

Article copyright:
© Copyright 1991
American Mathematical Society