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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Lagrangian circle actions

Clément Hyvrier

Algebraic & Geometric Topology 16 (2016) 1309–1342
Abstract

We consider paths of Hamiltonian diffeomorphisms preserving a given compact monotone lagrangian in a symplectic manifold that extend to an S1–Hamiltonian action. We compute the leading term of the associated lagrangian Seidel elements. We show that such paths minimize the lagrangian Hofer length. Finally, we apply these computations to lagrangian uniruledness and to give a nice presentation of the quantum cohomology of real lagrangians in monotone symplectic toric manifolds.

Keywords
Lagrangian quantum homology, Lagrangian Seidel element, monotone toric manifolds
Mathematical Subject Classification 2010
Primary: 53D12, 53D20, 57R17, 57R58
References
Publication
Received: 17 September 2013
Revised: 15 October 2015
Accepted: 24 November 2015
Published: 1 July 2016
Authors
Clément Hyvrier
Département de Mathématiques
Cégep Saint-Laurent
625 avenue Sainte-Croix
Montreal, QC H4L 3X7
Canada