## Duke Mathematical Journal

### Equivariant indices of $\operatorname{Spin}^{c}$-Dirac operators for proper moment maps

#### 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.

#### Article information

Source
Duke Math. J., Volume 166, Number 6 (2017), 1125-1178.

Dates
Revised: 27 May 2016
First available in Project Euclid: 13 January 2017

https://projecteuclid.org/euclid.dmj/1484276627

Digital Object Identifier
doi:10.1215/00127094-3792923

Mathematical Reviews number (MathSciNet)
MR3635901

Zentralblatt MATH identifier
1370.58010

#### Citation

Hochs, Peter; Song, Yanli. Equivariant indices of $\operatorname{Spin}^{c}$ -Dirac operators for proper moment maps. Duke Math. J. 166 (2017), no. 6, 1125--1178. doi:10.1215/00127094-3792923. https://projecteuclid.org/euclid.dmj/1484276627

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