Hamiltonian loops on the symplectic one-point blow up

We lift a loop of Hamiltonian diffeomorphisms on a symplectic manifold to loop of Hamiltonian diffeomorphisms on the symplectic one-point blow up of the symplectic manifold. Then we use Weinstein’s morphism to show that the lifted loop of Hamiltonian diffeomorphisms has infinite order on the fundamental group of the group of Hamiltonian diffeomorphisms of the blown up manifold.

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Received 30 September 2015

Accepted 8 December 2017

Published 26 November 2018