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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
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