The relative index theorem for general firstorder elliptic operators
Abstract
The relative index theorem is proved for general firstorder elliptic operators that are complete and coercive at infinity over measured manifolds. This extends the original result by GromovLawson for generalised Dirac operators as well as the result of BärBallmann for Diractype 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 firstorder elliptic operators due to BärBandara. Splitting, decomposition and the Phirelative index theorem are proved on route to the relative index theorem.
 Publication:

arXiv eprints
 Pub Date:
 November 2021
 arXiv:
 arXiv:2111.12352
 Bibcode:
 2021arXiv211112352B
 Keywords:

 Mathematics  Analysis of PDEs;
 Mathematics  Differential Geometry;
 Mathematics  Functional Analysis;
 58J20;
 58J32;
 58J90
 EPrint:
 doi:10.1007/s12220022010481