Grid diagrams and shellability

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.