Algebraic & Geometric Topology

The Seidel morphism of Cartesian products

Rémi Leclercq

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Abstract

We prove that the Seidel morphism of (M×M,ωω) 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].

Article information

Source
Algebr. Geom. Topol., Volume 9, Number 4 (2009), 1951-1969.

Dates
Received: 1 July 2009
Accepted: 31 August 2009
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513797071

Digital Object Identifier
doi:10.2140/agt.2009.9.1951

Mathematical Reviews number (MathSciNet)
MR2550462

Zentralblatt MATH identifier
1176.57027

Subjects
Primary: 57R17: Symplectic and contact topology
Secondary: 57R58: Floer homology 57S05: Topological properties of groups of homeomorphisms or diffeomorphisms

Keywords
symplectic manifolds Hamiltonian diffeomorphisms Seidelś morphism

Citation

Leclercq, Rémi. The Seidel morphism of Cartesian products. Algebr. Geom. Topol. 9 (2009), no. 4, 1951--1969. doi:10.2140/agt.2009.9.1951. https://projecteuclid.org/euclid.agt/1513797071


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