Vol. 290, No. 2, 2017

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Noncontractible Hamiltonian loops in the kernel of Seidel's representation

Sílvia Anjos and Rémi Leclercq

Vol. 290 (2017), No. 2, 257–272

The main purpose of this note is to exhibit a Hamiltonian diffeomorphism loop undetected by the Seidel morphism of a 1-parameter family of 2-point blow-ups of S2 × S2, exactly one of which is monotone. As side remarks, we show that Seidel’s morphism is injective on all Hirzebruch surfaces, and discuss how to adapt the monotone example to the Lagrangian setting.

symplectic geometry, Seidel morphism, toric symplectic manifolds, Hirzebruch surfaces
Mathematical Subject Classification 2010
Primary: 53D45
Secondary: 53D05, 57S05
Received: 6 April 2016
Revised: 9 March 2017
Accepted: 10 March 2017
Published: 25 July 2017
Sílvia Anjos
Center for Mathematical Analysis, Geometry and Dynamical Systems
Mathematics Department
Instituto Superior Técnico
Av. Rovisco Pais
1049-001 Lisboa
Rémi Leclercq
Laboratoire de Mathématiques d’Orsay
Université Paris-Sud, CNRS, Université Paris-Saclay
91405 Orsay