SIGMA 22 (2026), 051, 8 pages      arXiv:2601.07714      https://doi.org/10.3842/SIGMA.2026.051
Contribution to the Special Issue on Geometry and Dynamics in memory of Will Merry

A Note on Somewhere Positive Loops of Contactomorphisms

Igor Uljarević
Faculty of Mathematics, University of Belgrade, Studentski trg 16, 11158 Belgrade, Republic of Serbia

Received January 13, 2026, in final form May 06, 2026; Published online May 18, 2026

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.

Key words: contact rigidity; symplectic homology; quasi-measures.

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