Duke Mathematical Journal

Equivariant indices of Spinc-Dirac operators for proper moment maps

Peter Hochs and Yanli Song

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Abstract

We define an equivariant index of Spinc-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
Received: 25 March 2015
Revised: 27 May 2016
First available in Project Euclid: 13 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1484276627

Digital Object Identifier
doi:10.1215/00127094-3792923

Mathematical Reviews number (MathSciNet)
MR3635901

Zentralblatt MATH identifier
1370.58010

Subjects
Primary: 58J20: Index theory and related fixed point theorems [See also 19K56, 46L80]
Secondary: 53C27: Spin and Spin$^c$ geometry 53D20: Momentum maps; symplectic reduction

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

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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