Lagrangian circle actions

Hyvrier, Clément

doi:10.2140/agt.2016.16.1309

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Lagrangian circle actions

Clément Hyvrier

Algebraic & Geometric Topology 16 (2016) 1309–1342

DOI: 10.2140/agt.2016.16.1309

Abstract

We consider paths of Hamiltonian diffeomorphisms preserving a given compact monotone lagrangian in a symplectic manifold that extend to an $S^{1}$ –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

Volume 16, issue 3 (2016)