Grid diagrams and shellability

Details Grid diagrams and shellability Grid diagrams and shellability

2009-01-15

arxiv.org/abs/0901.2156v3

Mathematics

Geometric Topology

12 pages, 5 figures. An earlier version of this paper attempted to construct a stable homotopy type from a grid presentation o

Scientific paper

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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