Classification of invariant tight contact structures on the 3-space, -ball and -sphere
Geometric Topology
2026-01-21 v1 Differential Geometry
Abstract
We prove some classification results for tight contact structure in the 3-space, -ball and -sphere that are invariant with respect to some arbitrary involution, that is conjugated to the standard rotation around the x-axis. Unlike the classical scenario, a new integral torsion appears, dictating a splitting between equivalence classes. These tools could be useful fur future classification results regarding strongly invertible Legendrian knots.
Keywords
Cite
@article{arxiv.2601.14040,
title = {Classification of invariant tight contact structures on the 3-space, -ball and -sphere},
author = {Mirko Torresani},
journal= {arXiv preprint arXiv:2601.14040},
year = {2026}
}