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arXiv · 2111.12352

The relative index theorem for general first-order elliptic operators

Lashi Bandara
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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 Bär-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 Bär-Bandara. Splitting, decomposition and the Phi-relative index theorem are proved on route to the relative index theorem.

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Lashi Bandara. 2022-08-05. The relative index theorem for general first-order elliptic operators. https://doi.org/10.1007/s12220-022-01048-1

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