## Algebraic & Geometric Topology

### Lagrangian circle actions

Clément Hyvrier

#### 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.

#### Article information

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

Dates
Revised: 15 October 2015
Accepted: 24 November 2015
First available in Project Euclid: 28 November 2017

https://projecteuclid.org/euclid.agt/1511895847

Digital Object Identifier
doi:10.2140/agt.2016.16.1309

Mathematical Reviews number (MathSciNet)
MR3523040

Zentralblatt MATH identifier
1342.53102

#### Citation

Hyvrier, Clément. Lagrangian circle actions. Algebr. Geom. Topol. 16 (2016), no. 3, 1309--1342. doi:10.2140/agt.2016.16.1309. https://projecteuclid.org/euclid.agt/1511895847

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