Algebraic & Geometric Topology

Lagrangian circle actions

Clément Hyvrier

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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.

Article information

Algebr. Geom. Topol., Volume 16, Number 3 (2016), 1309-1342.

Received: 17 September 2013
Revised: 15 October 2015
Accepted: 24 November 2015
First available in Project Euclid: 28 November 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53D12: Lagrangian submanifolds; Maslov index 53D20: Momentum maps; symplectic reduction 57R17: Symplectic and contact topology 57R58: Floer homology

Lagrangian quantum homology Lagrangian Seidel element monotone toric manifolds


Hyvrier, Clément. Lagrangian circle actions. Algebr. Geom. Topol. 16 (2016), no. 3, 1309--1342. doi:10.2140/agt.2016.16.1309.

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