A short proof of an index theorem, II

2023/06/24 by Y. Abdolmaleki, Abdolmaleki, Y., Dan Kučerovský +1 · 1 citation
Mathematics · #19K56 #58J20 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Geometric and Algebraic Topology #K-Theory and Homology (math.KT)

paper · pdf · doi:10.48550/arxiv.2306.13987

openalex publication_date 2023/06/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce a slight modification of the usual equivariant KK-theory. We use this to give a KK-theoretical proof of an equivariant index theorem for Dirac-Schrodinger operators on a non-compact manifold of nowhere positive curvature. We incidentally show that the boundary of Dirac is Dirac; generalizing earlier work of Baum and coworkers, and a result of Higson and Roe.

Cited by

• Computing the K-homology K-theory product in splitexact algebraic KK-theory

Related

• Index theorem for equivariant Dirac operators on non-compact manifolds
• A partitioned manifold index theorem for noncompact hypersurfaces
• An absolute version of the Gromov-Lawson relative index theorem
• Equivariant APS index for Dirac operators of non-product type near the boundary
• Relative eta invariant and uniformly positive scalar curvature on non-compact manifolds