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On equivariant Euler characteristics. (English) Zbl 0708.19004
Let G be a finite group of symmetries of a compact manifold M. In string theory one uses an Euler characteristic based on simultaneous fixed-point sets of commuting pairs of elements of G. The authors show that this is the same as the Euler characteristic of the equivariant K-theory $$K^*_ G(M)$$. The method depends on expressing $$K^*_ G(M)$$ tensored with the complex numbers in terms of the non-equivariant K- theory of the fixed-point sets of single elements of G.
Reviewer: R.J.Steiner

##### MSC:
 19L47 Equivariant $$K$$-theory 55N91 Equivariant homology and cohomology in algebraic topology 81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
##### Keywords:
string theory; Euler characteristic; equivariant K-theory
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##### References:
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