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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Finite cyclic subgroups determine the spectrum of the equivariant $ K$-theory


Author: Agnieszka Bojanowska
Journal: Proc. Amer. Math. Soc. 113 (1991), 245-249
MSC: Primary 55N91; Secondary 19M05, 22E99, 55N15
MathSciNet review: 1064899
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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 $ K$-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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1064899-5
PII: S 0002-9939(1991)1064899-5
Article copyright: © Copyright 1991 American Mathematical Society