12-2023. Accepted in Alg. Geom. Topol.
The symplectic cohomology of certain symplectic manifolds $W$ with non-compact ends modelled on the positive symplectization of a compact contact manifold $Y$ is shown to vanish whenever there is a positive loop of contactomorphisms of $Y$ which extends to a loop of Hamiltonian diffeomorphisms of $W$. An open string version of this result is also proved: the wrapped Floer cohomology of a Lagrangian $L$ with ideal Legendrian boundary $Λ$ is shown to vanish if there is a positive loop $Λ_{t}$ based at $Λ$ which extends to an exact loop of Lagrangians based at $L$. Various examples of such loops are considered. Applications include the construction of exotic compactly supported symplectomorphisms and exotic fillings of $Λ$.
@unpublished{extensible-positive-loops,
author = {Dylan Cant and Jakob Hedicke and Eric Kilgore},
title = {Extensible positive loops and vanishing of symplectic cohomology},
note = {To appear in Alg. Geom. Topol.},
year = {2023},
eprint = {2311.18267},
archivePrefix = {arXiv},
primaryClass = {math.SG},
}