Grid diagrams and shellability

Sucharit Sarkar

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arXiv · 0901.2156

Grid diagrams and shellability

Sucharit Sarkar

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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.

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Sucharit Sarkar. 2009-01-15. Grid diagrams and shellability. https://arxiv.org/abs/0901.2156

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