Computing the Thurston-Bennequin invariant in open books
Geometric Topology
2026-02-10 v2 Symplectic Geometry
Abstract
We give explicit formulas and algorithms for the computation of the Thurston-Bennequin invariant of a nullhomologous Legendrian knot on a page of a contact open book and on contact Heegaard surfaces. Furthermore, we extend the results to rationally nullhomologous knots in arbitrary 3-manifolds.
Cite
@article{arxiv.1605.00794,
title = {Computing the Thurston-Bennequin invariant in open books},
author = {Sebastian Durst and Marc Kegel and Mirko Klukas},
journal= {arXiv preprint arXiv:1605.00794},
year = {2026}
}
Comments
17 pages, 8 figures; Version 2: Fixed two sign mistakes (one in the formula for the Heegaard splitting and one in the proof of the formula for the open books), shortened the example section