Homology, Homotopy and Applications

Volume 14 (2012)

Number 2

Grid diagrams and shellability

Pages: 77 – 90

DOI: https://dx.doi.org/10.4310/HHA.2012.v14.n2.a5

Author

Sucharit Sarkar (Department of Mathematics, Columbia University, New York)

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 S³, 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.

Keywords

knot Floer homology, shellable poset, grid diagram, flow category

2010 Mathematics Subject Classification

06A07, 57M25, 57R58

Published 4 December 2012