A Note on Somewhere Positive Loops of Contactomorphisms
Symplectic Geometry
2026-05-20 v2
Abstract
In this note, we consider contractible loops of contactomorphisms that are positive over some non-empty closed subset of a contact manifold. Such closed subsets are called immaterial. We argue that the complement of a Reeb-invariant immaterial subset can be seen as big in contact geometric terms. This is supported by two results: one regarding symplectic homology of the filling and the other regarding recently introduced contact quasi-measures.
Cite
@article{arxiv.2601.07714,
title = {A Note on Somewhere Positive Loops of Contactomorphisms},
author = {Igor Uljarević},
journal= {arXiv preprint arXiv:2601.07714},
year = {2026}
}