Braids and combinatorial knot Floer homology
Geometric Topology
2013-12-20 v1 Symplectic Geometry
Abstract
We present a braid-theoretic approach to combinatorially computing knot Floer homology. To a knot or link K, which is braided about the standard disk open book decomposition for (S^3,\xi_std), we associate a corresponding multi-pointed nice Heegaard diagram. We then describe an explicit algorithm for computing the associated knot Floer homology groups. We compute explicit bounds for the computational complexity of our algorithm and demonstrate that, in many cases, it is significantly faster than the previous approach using grid diagrams.
Keywords
Cite
@article{arxiv.1312.5586,
title = {Braids and combinatorial knot Floer homology},
author = {Peter Lambert-Cole and Michaela Stone and David Shea Vela-Vick},
journal= {arXiv preprint arXiv:1312.5586},
year = {2013}
}
Comments
18 pages, 8 figures