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arXiv · 2610.09812

A secondary index map on relative K-homology

Matti Lyko
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Abstract

We introduce a secondary index map from relative K-homology to the K-theory of a relative structure algebra. We prove an algebraic Mayer-Vietoris sequence for the relative structure algebra, and prove compatibility of the secondary index map with the Mayer-Vietoris boundary map. As an application, we compute the secondary index of the Dirac operator on an even-dimensional spin manifold with collared metric having uniformly positive scalar curvature on the boundary. This computation leads to a refinement of the delocalized APS-index theorem.

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Matti Lyko. 2026-10-07. A secondary index map on relative K-homology. https://arxiv.org/abs/2610.09812

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