The Seidel morphism of Cartesian products

Leclercq, Rémi

doi:10.2140/agt.2009.9.1951

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The Seidel morphism of Cartesian products

Rémi Leclercq

Algebraic & Geometric Topology 9 (2009) 1951–1969

DOI: 10.2140/agt.2009.9.1951

Abstract

We prove that the Seidel morphism of $(M \times M^{'}, ω \oplus ω^{'})$ 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].

Keywords

symplectic manifolds, Hamiltonian diffeomorphisms, Seidelś morphism

Mathematical Subject Classification 2000

Primary: 57R17

Secondary: 57R58, 57S05

References

Publication

Received: 1 July 2009

Accepted: 31 August 2009

Published: 3 October 2009

Authors

Rémi Leclercq
Max-Planck-Institut für Mathematik in den Naturwissenschaften Inselstraße 22 04103 Leipzig Germany
http://personal-homepages.mis.mpg.de/leclercq/

Volume 9, issue 4 (2009)