Equivariant indices of Spinc-Dirac operators for proper moment maps

Peter Hochs; Yanli Song

doi:10.1215/00127094-3792923

Abstract

We define an equivariant index of $\operatorname{Spin}^{c}$ -Dirac operators on possibly noncompact manifolds, acted on by compact, connected Lie groups. Our main result is that the index decomposes into irreducible representations according to the quantization commutes with reduction principle.

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Peter Hochs. Yanli Song. "Equivariant indices of $\operatorname{Spin}^{c}$ -Dirac operators for proper moment maps." Duke Math. J. 166 (6) 1125 - 1178, 15 April 2017. https://doi.org/10.1215/00127094-3792923

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Received: 25 March 2015; Revised: 27 May 2016; Published: 15 April 2017

First available in Project Euclid: 13 January 2017

zbMATH: 1370.58010

MathSciNet: MR3635901

Digital Object Identifier: 10.1215/00127094-3792923

Subjects:

Primary: 58J20

Secondary: 53C27 , 53D20

Keywords: ${\operatorname{Spin}}^{c}$-Dirac operator , Index theory , moment map , proper group action

Abstract

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