Geodesic
The Seidel morphism of Cartesian products
Leclercq, Rémi1
1Max-Planck-Institut für Mathematik in den Naturwissenschaften, Inselstraße 22, 04103 Leipzig, Germany
Algebraic and Geometric Topology, Tome 9 (2009) no. 4, pp. 1951-1969
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We prove that the Seidel morphism of (M × M′,ω ⊕ ω′) is naturally related to the Seidel morphisms of (M,ω) and (M′,ω′), when these manifolds are monotone. We deduce that any homotopy class of loops of Hamiltonian diffeomorphisms of one component, with nontrivial image via Seidel’s morphism, leads to an injection of the fundamental group of the group of Hamiltonian diffeomorphisms of the other component into the fundamental group of the group of Hamiltonian diffeomorphisms of the product. This result was inspired by and extends results obtained by Pedroza [Int. Math. Res. Not. (2008) Art. ID rnn049].

DOI : 10.2140/agt.2009.9.1951
Keywords: symplectic manifolds, Hamiltonian diffeomorphisms, Seidelś morphism

Leclercq, Rémi  1

1 Max-Planck-Institut für Mathematik in den Naturwissenschaften, Inselstraße 22, 04103 Leipzig, Germany 
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Leclercq, Rémi. The Seidel morphism of Cartesian products. Algebraic and Geometric Topology, Tome 9 (2009) no. 4, pp. 1951-1969. doi: 10.2140/agt.2009.9.1951

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