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An L2-Index Theorem for Dirac Operators on S1×R3

✍ Scribed by Tom M.W. Nye; Michael A. Singer

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 178 KB
Volume: 177
Category: Article
ISSN: 0022-1236
DOI: 10.1006/jfan.2000.3648

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✦ Synopsis

An expression is found for the L 2 -index of a Dirac operator coupled to a connection on a U n vector bundle over S 1 _R 3 . 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 S 1 . An excision theorem due to Gromov, Lawson, and Anghel reduces the index theorem to this special case.

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