Year: 2009
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Sarkar, Sucharit
Institution: Columbia University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2950740368