Lagrangian circle actions

Hyvrier, Clément¹

¹Département de Mathématiques, Cégep Saint-Laurent, 625 avenue Sainte-Croix, Montreal, QC H4L 3X7, Canada

Algebraic and Geometric Topology, Tome 16 (2016) no. 3, pp. 1309-1342

Résumé

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.

Détail

DOI : 10.2140/agt.2016.16.1309

Classification : 53D12, 53D20, 57R17, 57R58
Keywords: Lagrangian quantum homology, Lagrangian Seidel element, monotone toric manifolds

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