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The Relative Index Theorem for General First-Order Elliptic Operators

Version 2 2024-05-31, 00:14
Version 1 2023-11-03, 03:55
journal contribution
posted on 2024-05-31, 00:14 authored by Lashi BandaraLashi Bandara
AbstractThe 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.

History

Journal

Journal of Geometric Analysis

Volume

33

Article number

10

Pagination

1-20

Location

Berlin, Germany

ISSN

1050-6926

eISSN

1559-002X

Language

English

Publication classification

C1.1 Refereed article in a scholarly journal

Issue

1

Publisher

Springer