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June 2007 A compact symplectic four-manifold admits only finitely many inequivalent toric actions
Yael Karshon, Liat Kessler, Martin Pinsonnault
J. Symplectic Geom. 5(2): 139-166 (June 2007).

Abstract

Let ($M$, \omega) be a four-dimensional compact connected symplectic manifold. We prove that ($M$, \omega) admits only finitely many inequivalent Hamiltonian effective 2-torus actions. Consequently, if $M$ is simply connected, the number of conjugacy classes of 2-tori in the symplectomorphism group Sympl($M$, \omega) is finite. Our proof is “soft”. The proof uses the fact that if a symplectic four-manifold admits a toric action, then the restriction of the period map to the set of exceptional homology classes is proper. In an appendix, we present the Gromov–McDuff properness result for a general compact symplectic four-manifold.

Citation

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Yael Karshon. Liat Kessler. Martin Pinsonnault. "A compact symplectic four-manifold admits only finitely many inequivalent toric actions." J. Symplectic Geom. 5 (2) 139 - 166, June 2007.

Information

Published: June 2007
First available in Project Euclid: 3 February 2008

zbMATH: 1136.53060
MathSciNet: MR2377250

Rights: Copyright © 2007 International Press of Boston

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Vol.5 • No. 2 • June 2007
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