Grid diagrams and shellability
Geometric Topology
2010-11-29 v3
Abstract
We explore a somewhat unexpected connection between knot Floer homology and shellable posets, via grid diagrams. Given a grid presentation of a knot K inside S^3, we define a poset which has an associated chain complex whose homology is the knot Floer homology of K. We then prove that the closed intervals of this poset are shellable. This allows us to combinatorially associate a PL flow category to a grid diagram.
Keywords
Cite
@article{arxiv.0901.2156,
title = {Grid diagrams and shellability},
author = {Sucharit Sarkar},
journal= {arXiv preprint arXiv:0901.2156},
year = {2010}
}
Comments
12 pages, 5 figures. An earlier version of this paper attempted to construct a stable homotopy type from a grid presentation of a knot, but there was a crucial mistake. In this revised version, we construct a flow category from a grid diagram