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2011 Symplectic manifolds with vanishing action–Maslov homomorphism
Mark Branson
Algebr. Geom. Topol. 11(2): 1077-1096 (2011). DOI: 10.2140/agt.2011.11.1077

Abstract

The action–Maslov homomorphism I:π1(Ham(X,ω)) is an important tool for understanding the topology of the Hamiltonian group of monotone symplectic manifolds. We explore conditions for the vanishing of this homomorphism, and show that it is identically zero when the Seidel element has finite order and the homology satisfies property D (a generalization of having homology generated by divisor classes). We use these results to show that I=0 for products of projective spaces and the Grassmannian of 2 planes in 4.

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Mark Branson. "Symplectic manifolds with vanishing action–Maslov homomorphism." Algebr. Geom. Topol. 11 (2) 1077 - 1096, 2011. https://doi.org/10.2140/agt.2011.11.1077

Information

Received: 2 November 2010; Revised: 31 January 2011; Accepted: 3 February 2011; Published: 2011
First available in Project Euclid: 19 December 2017

zbMATH: 1220.53100
MathSciNet: MR2792374
Digital Object Identifier: 10.2140/agt.2011.11.1077

Subjects:
Primary: 53D45
Secondary: 20F69, 53D35, 53D40

Rights: Copyright © 2011 Mathematical Sciences Publishers

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Vol.11 • No. 2 • 2011
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