A Note on Somewhere Positive Loops of Contactomorphisms

2026/01/12 by Igor Uljarević · 1 voice
Mathematics · #math.SG

paper · pdf · doi:10.3842/sigma.2026.051

arxiv published 2026/01/12 · arxiv updated 2026/05/18

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.

Citations

• Quantitative contact Hamiltonian dynamics
• Contact big fiber theorems
• Remarks on eternal classes in symplectic cohomology
• Quantitative characterization in contact Hamiltonian dynamics -- I
• Maximum principles in symplectic homology
• Quasi-morphisms and quasi-states in symplectic topology
• Symplectic quasi-states and semi-simplicity of quantum homology
• A biased view of symplectic cohomology
• Rigid subsets of symplectic manifolds
• Geometry of contact transformations and domains: orderability versus squeezing
• Quasi-states and symplectic intersections
• Construction of spectral invariants of Hamiltonian paths on closed symplectic manifolds
• Partially ordered groups and geometry of contact transformations
• Floer homology and Novikov rings

Discussions

• Igor Uljarevi\'c: A note on somewhere positive loops of contactomorphisms https://arxiv.org/abs/2601.07714 https://arxiv.org/pdf/2601.07714 https://arxiv.org/html/2601.07714 [bsky, 0 points, 0 comments]

Related

• Contact quasi-states and their applications
• Orderable Contact Structures on Liouville-fillable Contact Manifolds
• On manifolds with infinitely many fillable contact structures
• Automatic transversality in contact homology I: Regularity
• Translated points on hypertight contact manifolds