MPS-RR 1999-34
October 1999

Atiyah-Patodi-Singer Type Index Theorems for Manifolds with Corners and Splitting of j-Invariants I

by:

Gorm Salomonsen

Abstract

We construct self-adjoint extensions of Dirac operators on manifolds with corners of codimension 2, which generalize the Atiyah-Patodi-Singer boundary condition. The boundary conditions are related to geometric constructions, which convert problems on manifolds with corners into problems on manifolds with boundary and wedge singularities. In the case, where the Dirac bundle is a super-bundle, we prove two general index theorems, which differ by the splitting formula for j-invariants. Further we work out the de Rham, signature and twisted spin complex in closer detail. Finally we give a new proof of the splitting formula for the j-invariant.

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This paper has now been published in Geom. Funct. Anal. 11, 1031--1095 (2001)