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
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.

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