PreprintCC BY 4.0arXiv
A secondary index map on relative K-homology
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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BibTeX
@misc{lyko2026secondary,
title = {{A secondary index map on relative K-homology}},
author = {Matti Lyko},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.09812},
eprint = {2610.09812},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.09812},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A secondary index map on relative K-homology
AU - Matti Lyko
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.09812
UR - https://arxiv.org/abs/2610.09812
AB - 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.
ER -