English

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.

Keywords

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

R2 v1 2026-06-22T23:35:31.459Z