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.
Citation
Sucharit Sarkar. "Grid diagrams and shellability." Homology Homotopy Appl. 14 (2) 77 - 90, 2012.
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