Hamiltonian perturbations in contact Floer homology

Abstract

We study the contact Floer homology ${\mathrm{HF}}_{\ast }(W,h)$ introduced by Merry-Uljarević, which associates a Floer-type homology theory to a Liouville domain $W$ and a contact Hamiltonian $h$ on its boundary. The main results investigate the behavior of ${\mathrm{HF}}_{\ast }(W,h)$ under the perturbations of the input contact Hamiltonian $h$. In particular, we provide sufficient conditions that guarantee ${\mathrm{HF}}_{\ast }(W,h)$ to be invariant under the perturbations. This can be regarded as a contact geometry analogue of the continuation and bifurcation maps along the Hamiltonian perturbations of Hamiltonian Floer homology in symplectic geometry. As an application, we give an algebraic proof of a rigidity result concerning the positive loops of contactomorphisms for a wide class of contact manifolds.

19 pages

References in corpus (1)

• Exotic symplectomorphisms and contact circle actions

Cited by in corpus (1)

• Selective symplectic homology with applications to contact non-squeezing