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Abstract: This is a sequel to the paper -The signature package on Witt spaces, I. Indexclasses- by the same authors. In the first part we investigated, via aparametrix construction, the regularity properties of the signature operator ona stratified Witt pseudomanifold, proving, in particular, that one can define aK-homology signature class. We also established the existence of an analyticindex class for the signature operator twisted by a C^* r\Gamma Mischenkobundle and proved that the K-homology signature class is mapped to thesignature index class by the assembly map. In this paper we continue our study,showing that the signature index class is invariant under rational Wittbordisms and stratified homotopies. We are also able to identify this analyticclass with the topological analogue of the Mischenko symmetric signaturerecently defined by Banagl. Finally, we define Witt-Novikov higher signaturesand show that our analytic results imply a purely topological theorem, namelythat the Witt-Novikov higher signatures are stratified homotopy invariants ifthe assembly map in K-theory is rationally injective.



Author: Pierre Albin, Eric Leichtnam, Rafe Mazzeo, Paolo Piazza

Source: https://arxiv.org/







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