An L2-Index Theorem for Dirac Operators on S1×[formula omitted]3

An expression is found for the L2-index of a Dirac operator coupled to a connection on a Un vector bundle over S1×R3. Boundary conditions for the connection are given which ensure the coupled Dirac operator Fredholm. Callias' index theorem is used to calculate the index when the connection is i...

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Bibliographic Details
Published in:Journal of functional analysis 2000-10, Vol.177 (1), p.203-218
Main Authors: Nye, Tom M.W., Singer, Michael A.
Format: Article
Language:English
Subjects:
connection
Dirac operator
elliptic operator
excision
L2-index theorem
manifold with boundary
Online Access:Get full text
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Summary:An expression is found for the L2-index of a Dirac operator coupled to a connection on a Un vector bundle over S1×R3. Boundary conditions for the connection are given which ensure the coupled Dirac operator Fredholm. Callias' index theorem is used to calculate the index when the connection is independent of the coordinate on S1. An excision theorem due to Gromov, Lawson, and Anghel reduces the index theorem to this special case.
ISSN:0022-1236
1096-0783
DOI:10.1006/jfan.2000.3648