Lefschetz numbers for C*-algebras

Details Lefschetz numbers for C*-algebras Lefschetz numbers for C*-algebras

2007-08-31

arxiv.org/abs/0708.4278v4

Mathematics

K-Theory and Homology

Rewritten for style, minor errors corrected

Scientific paper

Using Poincare duality, we formulate a formula of Lefschetz type which computes the Lefschetz number of an endomorphism of a separable, nuclear C*-algebra satisfying Poincare duality and the Kunneth theorem. (The Lefschetz number of an endomorphism is the graded trace of the induced map on K-theory tensored with the complex numbers, as in the classical case.) We then consider endomorphisms of Cuntz-Krieger algebras O_A. An endomorphism has an invariant, which is a permutation of an infinite set, and the contracting and expanding behavior of this permutation describes the Lefschetz number of the endomorphism. Using this description we derive a closed polynomial formula for the Lefschetz number depending on the matrix A and the presentation of the endomorphism.

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