Computing rotation numbers in open books
Geometric Topology
2026-02-10 v3 Symplectic Geometry
Abstract
We give explicit formulas and algorithms for the computation of the rotation number of a nullhomologous Legendrian knot on a page of a contact open book. On the way, we derive new formulas for the computation of the Thurston-Bennequin invariant of such knots and the Euler class and the d3-invariant of the underlying contact structure.
Cite
@article{arxiv.1801.01034,
title = {Computing rotation numbers in open books},
author = {Sebastian Durst and Marc Kegel},
journal= {arXiv preprint arXiv:1801.01034},
year = {2026}
}
Comments
20 pages, 7 figures; v.2: minor changes and clarifications; v.3: changed Example 1.3 and corrected the definition of Q in Algorithm 6.1