Volume 15, issue 3 (2011)

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Homological Lagrangian monodromy

Shengda Hu, François Lalonde and Rémi Leclercq

Geometry & Topology 15 (2011) 1617–1650

We show that the Hamiltonian Lagrangian monodromy group, in its homological version, is trivial for any weakly exact Lagrangian submanifold of a symplectic manifold. The proof relies on a sheaf approach to Floer homology given by a relative Seidel morphism.

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Lagrangian monodromy, Hamiltonian isotopy, Hamiltonian fibration, Floer homology, relative Seidel morphism
Mathematical Subject Classification 2010
Primary: 53D12, 53D40
Secondary: 53C15, 53D45, 57R58, 57S05, 58B20
Received: 4 March 2010
Revised: 30 June 2011
Accepted: 2 August 2011
Published: 26 September 2011
Proposed: Leonid Polterovich
Seconded: Yasha Eliashberg, Simon Donaldson
Shengda Hu
Department of Mathematics
Wilfrid Laurier University
75 University Ave. West
Ontario N2L 3C5
François Lalonde
Département de mathématiques et de Statistique
Université de Montréal
C.P. 6128
Succ. Centre-ville
Québec H3C 3J7
Rémi Leclercq
Département de mathématiques et de Statistique
Université de Montréal
C.P. 6128
Succ. Centre-ville
Québec H3C 3J7