New Proof of the Cobordism Invariance of the Index

2000/11/28 by Maxim Braverman, Braverman, Maxim · 1 citation
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Spectral Theory (math.SP) #math.DG #math.SP

paper · pdf · doi:10.48550/arxiv.math/0011237

Some references are added, some minor changes are made. To appear in Proc. of AMS

arxiv created 2001/01/11 · arxiv updated 2009/11/30

Abstract

We give a simple proof of the cobordism invariance of the index of an elliptic operator. The proof is based on a study of a Witten-type deformation of an extension of the operator to a complete Riemannian manifold. One of the advantages of our approach is that it allows to treat directly general elliptic operator which are not of Dirac type.

Cited by

• The semi-classical Weyl law on complete manifolds

Related

• Cobordism invariance of the index for realizations of elliptic operators revisited
• Cobordism Invariance of the Index of Callias-Type Operators
• Orbifold Index Cobordism Invariance
• Families Index for Pseudodifferential Operators on Manifolds with Boundary
• The eta invariant and equivariant index of transversally elliptic operators