2007/08/31 by Siegfried Echterhoff, Echterhoff, Siegfried, Heath Emerson +3
Computer Science · Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Matrix Theory and Algorithms #math.KT #math.OA #msc:19K35 #msc:46L80
paper · pdf · doi:10.48550/arxiv.0708.4279
26 pages
arxiv created 2008/05/29 · arxiv updated 2009/12/01
Using Poincaré duality in K-theory, we state and prove a Lefschetz fixed point formula for endomorphisms of cross product C*-algebras C0(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 C0(X)\cross G induced by the endomorphism, 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 Poincaé duality and the formal Lefschetz lemma of the second author.