The Seidel morphism of cartesian products

Details The Seidel morphism of cartesian products The Seidel morphism of cartesian products

2009-03-23

arxiv.org/abs/0903.3742v2

Algebraic & Geometric Topology, 9 (2009), pp. 1951-1969

Mathematics

Symplectic Geometry

15 pages, no figure; v2: Abstract precised, typos corrected, references added

Scientific paper

10.2140/agt.2009.9.1951

We prove that the Seidel morphism of $(M \times M', \omega \oplus \omega')$ is naturally related to the Seidel morphisms of $(M,\omega)$ and $(M',\omega')$, when these manifolds are monotone. We deduce that any homotopy class of loops of Hamiltonian diffeomorphisms of one component, with non-trivial 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 [P08].

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