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Equivariant $\eta$ -invariants on homogeneous spaces

Equivariant $\eta$ -invariants on homogeneous spaces Let D be a homogeneous Dirac operator on the quotient M = G/H of two compact connected Lie groups. We construct a deformation $\tilde D$ ofD and calculate its equivariant $\eta$ -invariant $\eta_G(\tilde D)$ explicitly on the dense subset $G_0$ of G that acts freely onM. On $G_0$ , $\eta_G(\tilde D)$ and $\eta_G(D)$ differ only by a virtual character of $G$ . Moreover, if $G\supset H$ is a symmetric pair or if D is the untwisted Dirac operator, then $\eta_G(D)=\eta_G(\tilde D)$ on $G_0$ . We also sketch some applications of $\eta_G(\tilde D)$ . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematische Zeitschrift Springer Journals

Equivariant $\eta$ -invariants on homogeneous spaces

Goette, Sebastian
Mathematische Zeitschrift , Volume 232 (1) – Sep 1, 1999
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References (14)

Publisher
Springer Journals
Copyright
Copyright © 1999 by Springer-Verlag Berlin Heidelberg
Subject
Legacy
ISSN
0025-5874
eISSN
1432-1823
DOI
10.1007/PL00004757
Publisher site
See Article on Publisher Site

Abstract

Let D be a homogeneous Dirac operator on the quotient M = G/H of two compact connected Lie groups. We construct a deformation $\tilde D$ ofD and calculate its equivariant $\eta$ -invariant $\eta_G(\tilde D)$ explicitly on the dense subset $G_0$ of G that acts freely onM. On $G_0$ , $\eta_G(\tilde D)$ and $\eta_G(D)$ differ only by a virtual character of $G$ . Moreover, if $G\supset H$ is a symmetric pair or if D is the untwisted Dirac operator, then $\eta_G(D)=\eta_G(\tilde D)$ on $G_0$ . We also sketch some applications of $\eta_G(\tilde D)$ .

Journal

Mathematische Zeitschrift – Springer Journals

Published: Sep 1, 1999

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