Transverse braids and combinatorial knot Floer homology
Symplectic Geometry
2017-03-21 v1 Geometric Topology
Abstract
We describe a new method for combinatorially computing the transverse invariant in knot Floer homology. Previous work of the authors and Stone used braid diagrams to combinatorially compute knot Floer homology of braid closures. However, that approach was unable to explicitly identify the invariant of transverse links that naturally appears in braid diagrams. In this paper, we improve the previous approach in order to compute the transverse invariant. We define a new combinatorial complex that computes knot Floer homology and identify the BRAID invariant of transverse knots and links in the homology of this complex.
Keywords
Cite
@article{arxiv.1703.06861,
title = {Transverse braids and combinatorial knot Floer homology},
author = {Peter Lambert-Cole and David Shea Vela-Vick},
journal= {arXiv preprint arXiv:1703.06861},
year = {2017}
}
Comments
14 pages, 4 figures