Geodesic
Symplectic manifolds with vanishing action–Maslov homomorphism
Branson, Mark1
1Department of Mathematics, The Technion, Israeli Institute of Technology, Haifa, 32000, Israel
Algebraic and Geometric Topology, Tome 11 (2011) no. 2, pp. 1077-1096
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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.

DOI : 10.2140/agt.2011.11.1077
Keywords: action–Maslov, quantum homology, floer theory, Seidel homomorphism, symplectic geometry

Branson, Mark  1

1 Department of Mathematics, The Technion, Israeli Institute of Technology, Haifa, 32000, Israel 
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Branson, Mark. Symplectic manifolds with vanishing action–Maslov homomorphism. Algebraic and Geometric Topology, Tome 11 (2011) no. 2, pp. 1077-1096. doi: 10.2140/agt.2011.11.1077

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