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Cobordism for Hamiltonian loop group actions and flat connections on the punctured two-sphere

Cobordism for Hamiltonian loop group actions and flat connections on the punctured two-sphere We develop a theory of symplectic cobordism and a Duistermaat-Heckman principle for Hamiltonian loop group actions. As an application, we construct a symplectic cobordism between moduli spaces of flat connections on the three holed sphere and disjoint unions of toric varieties. This cobordism yields formulas for the mixed Pontrjagin numbers of the moduli spaces, equivalent to Witten's formulas in the case of symplectic volumes. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematische Zeitschrift Springer Journals

Cobordism for Hamiltonian loop group actions and flat connections on the punctured two-sphere

Meinrenken, E.; Woodward, C.
Mathematische Zeitschrift , Volume 231 (1) – May 1, 1999
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36 pages

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References (16)

Publisher
Springer Journals
Copyright
Copyright © 1999 by Springer-Verlag Berlin Heidelberg
Subject
Legacy
ISSN
0025-5874
eISSN
1432-1823
DOI
10.1007/PL00004718
Publisher site
See Article on Publisher Site

Abstract

We develop a theory of symplectic cobordism and a Duistermaat-Heckman principle for Hamiltonian loop group actions. As an application, we construct a symplectic cobordism between moduli spaces of flat connections on the three holed sphere and disjoint unions of toric varieties. This cobordism yields formulas for the mixed Pontrjagin numbers of the moduli spaces, equivalent to Witten's formulas in the case of symplectic volumes.

Journal

Mathematische Zeitschrift – Springer Journals

Published: May 1, 1999

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