2007/01/26 by Ulrich Bunke, Bunke, Ulrich
Mathematics · #58J20 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)
paper · pdf · doi:10.48550/arxiv.math/0701768
openalex publication_date 2007/01/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a invariant Dirac operator D on a manifold with a proper and cocompact action of a discrete group G. It gives rise to an equivariant K-homology class [D]. We show how the index of the induced orbifold Dirac operator can be calculated from [D] via the assembly map. We further derive a formula for this index in terms of the contributions of finite cyclic subgroups of G. According to results of W. Lueck, the equivariant K-homology can rationally be decomposed as a direct sum of contributions of finite cyclic subgroups of G. Our index formula thus leads to an explicit decomposition of the class [D].