Communications in Mathematical Physics

, Volume 107, Issue 3, pp 391-409

First online:

Proof of character-valued index theorems

  • Mark W. GoodmanAffiliated withJoseph Henry Laboratories, Princeton University

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A character-valued index is a generalization of the ordinary Dirac index to manifolds with nontrivial automorphism groups. A simple proof of the corresponding fixed-point theorem is presented which uses the techniques of supersymmetric quantum mechanics. This theorem relates the character-valued index to a topological integral of curvature forms on the fixed-point space of the automorphism in question.