2006/12/15 by Paulo Carrillo Rouse, Rouse, Paulo Carrillo
Mathematics · #19-06 #19K56 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #math.KT #msc:19-06 #msc:19K56
paper · pdf · doi:10.48550/arxiv.math/0612455
13 pages. To be submitted for the Proceedings of the International conference on K-theory and Non commutative geometry held in Valladolid, 2006
arxiv created 2006/12/15 · openalex publication_date 2006/12/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a Lie groupoid there is an analytic index morphism which takes values in the K-theory of the C^*-algebra associated to the groupoid. This is a good invariant but extracting numerical invariants from it, with the existent tools, is very difficult. In this work, we define another analytic index morphism associated to a Lie groupoid; this one takes values in a group that allows us to do pairings with cyclic cocycles. This last group is related to the compactly supported functions on the groupoid. We use the tangent groupoid to define our index as a sort of ''deformation''.