Cauchy data spaces and Atiyah-Patodi-Singer index on non-compact manifolds

TL;DR

This paper investigates the Cauchy data spaces of Callias-type operators on non-compact manifolds to better understand the Atiyah-Patodi-Singer index and elliptic boundary value problems.

Contribution

It introduces a framework for analyzing Cauchy data spaces of Callias-type operators on non-compact manifolds with boundary.

Findings

Characterization of Cauchy data spaces for Callias-type operators

Insights into the Atiyah-Patodi-Singer index on non-compact manifolds

Development of elliptic boundary value problem techniques for non-compact settings

Abstract

We study the Cauchy data spaces of the strongly Callias-type operators using maximal domain on manifolds with non-compact boundary, with the aim of understanding the Atiyah-Patodi-Singer index and elliptic boundary value problems.