Homology, Homotopy and Applications
- Homology Homotopy Appl.
- Volume 14, Number 2 (2012), 77-90.
Grid diagrams and shellability
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.
Homology Homotopy Appl., Volume 14, Number 2 (2012), 77-90.
First available in Project Euclid: 12 December 2012
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Sarkar, Sucharit. Grid diagrams and shellability. Homology Homotopy Appl. 14 (2012), no. 2, 77--90. https://projecteuclid.org/euclid.hha/1355321481