Algebraic & Geometric Topology 11 (2011) 1077–1096

DOI: 10.2140/agt.2011.11.1077

Abstract

The action–Maslov homomorphism I : π₁(Ham(X,ω)) → R 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 C⁴.

Keywords

action–Maslov, quantum homology, floer theory, Seidel homomorphism, symplectic geometry

Mathematical Subject Classification

Primary: 53D45

Secondary: 20F69, 53D35, 53D40

References

Publication

Received: 2 November 2010
Revised: 31 January 2011
Accepted: 3 February 2011
Published: 30 March 2011

Authors