The relative index theorem for general first-order elliptic operators
Analysis of PDEs
2022-10-31 v2 Differential Geometry
Functional Analysis
Abstract
The relative index theorem is proved for general first-order elliptic operators that are complete and coercive at infinity over measured manifolds. This extends the original result by Gromov-Lawson for generalised Dirac operators as well as the result of B\"ar-Ballmann for Dirac-type operators. The theorem is seen through the point of view of boundary value problems, using the graphical decomposition of elliptically regular boundary conditions for general first-order elliptic operators due to B\"ar-Bandara. Splitting, decomposition and the Phi-relative index theorem are proved on route to the relative index theorem.
Keywords
Cite
@article{arxiv.2111.12352,
title = {The relative index theorem for general first-order elliptic operators},
author = {Lashi Bandara},
journal= {arXiv preprint arXiv:2111.12352},
year = {2022}
}