A Lefschetz fixed-point formula for certain orbifold C*-algebras

Details A Lefschetz fixed-point formula for certain orbifold C*-algebras A Lefschetz fixed-point formula for certain orbifold C*-algebras

2007-08-31

arxiv.org/abs/0708.4279v2

Mathematics

K-Theory and Homology

26 pages

Scientific paper

Using Poincar\'e duality in K-theory, we state and prove a Lefschetz fixed point formula for endomorphisms of cross product C*-algebras $C_0(X)\cross G$ coming from covariant pairs. Here $G$ is assumed countable, $X$ a manifold, and $X\cross G$ cocompact and proper. The formula in question expresses the graded trace of the map on rationalized K-theory of $C_0(X)\cross G$ induced by the endomorphism, \emph{i.e.} the Lefschetz number, in terms of fixed orbits and representation-theoretic data connected with certain isotropy subgroups of the isotropy group at that point. The technique is to use noncommutative Poinca\'e duality and the formal Lefschetz lemma of the second author.

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