2009/11/04 by Pierre Albin, Éric Leichtnam, Eric Leichtnam +6 · 1 citation
Mathematics · #19K56 #58A35 #58J20 #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Operator Algebras (math.OA) #math.DG #math.KT #math.OA #msc:19K56 #msc:58A35 #msc:58J20
paper · pdf · doi:10.48550/arxiv.0911.0888
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openalex publication_date 2009/11/04 · arxiv created 2009/11/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This is a sequel to the paper "The signature package on Witt spaces, I. Index classes" by the same authors. In the first part we investigated, via a parametrix construction, the regularity properties of the signature operator on a stratified Witt pseudomanifold, proving, in particular, that one can define a K-homology signature class. We also established the existence of an analytic index class for the signature operator twisted by a C^*rΓMischenko bundle and proved that the K-homology signature class is mapped to the signature index class by the assembly map. In this paper we continue our study, showing that the signature index class is invariant under rational Witt bordisms and stratified homotopies. We are also able to identify this analytic class with the topological analogue of the Mischenko symmetric signature recently defined by Banagl. Finally, we define Witt-Novikov higher signatures and show that our analytic results imply a purely topological theorem, namely that the Witt-Novikov higher signatures are stratified homotopy invariants if the assembly map in K-theory is rationally injective.