Duke Mathematical Journal

Equivariant indices of Spinc-Dirac operators for proper moment maps

Peter Hochs and Yanli Song

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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

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

Received: 25 March 2015
Revised: 27 May 2016
First available in Project Euclid: 13 January 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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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