#### Vol. 290, No. 2, 2017

 Recent Issues Vol. 291: 1  2 Vol. 290: 1  2 Vol. 289: 1  2 Vol. 288: 1  2 Vol. 287: 1  2 Vol. 286: 1  2 Vol. 285: 1  2 Vol. 284: 1  2 Online Archive Volume: Issue:
 The Journal Subscriptions Editorial Board Officers Special Issues Submission Guidelines Submission Form Contacts Author Index To Appear ISSN: 0030-8730
Noncontractible Hamiltonian loops in the kernel of Seidel's representation

### Sílvia Anjos and Rémi Leclercq

Vol. 290 (2017), No. 2, 257–272
##### Abstract

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 ${S}^{2}×{S}^{2}$, 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.

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