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Abstract
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We prove that the Seidel morphism of
is naturally related to the Seidel morphisms of
and
, 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].
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Keywords
symplectic manifolds, Hamiltonian diffeomorphisms, Seidelś
morphism
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Mathematical Subject Classification 2000
Primary: 57R17
Secondary: 57R58, 57S05
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Publication
Received: 1 July 2009
Accepted: 31 August 2009
Published: 3 October 2009
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