English

Computing rotation and self-linking numbers in contact surgery diagrams

Geometric Topology 2017-09-01 v4 Symplectic Geometry

Abstract

We give an explicit formula to compute the rotation number of a nullhomologous Legendrian knot in contact (1/n)-surgery diagrams along Legendrian links and obtain a corresponding result for the self-linking number of transverse knots. Moreover, we extend the formula by Ding-Geiges-Stipsicz for computing the d3-invariant to (1/n)-surgeries.

Keywords

Cite

@article{arxiv.1605.00795,
  title  = {Computing rotation and self-linking numbers in contact surgery diagrams},
  author = {Sebastian Durst and Marc Kegel},
  journal= {arXiv preprint arXiv:1605.00795},
  year   = {2017}
}

Comments

19 pages, 6 figures; V2: Added the section on the d3-invariant and fixed a few misprints; V3: Minor corrections and clarifications; V4: Added a missing "n" in the formula for computing the Euler class of the contact structure in Theorem 5.1

R2 v1 2026-06-22T13:51:55.528Z