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.
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