Homology, Homotopy and Applications

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.

Article information

Source
Homology Homotopy Appl., Volume 14, Number 2 (2012), 77-90.

Dates
First available in Project Euclid: 12 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.hha/1355321481

Mathematical Reviews number (MathSciNet)
MR3007086

Zentralblatt MATH identifier
1275.57022

Subjects
Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45} 06A07: Combinatorics of partially ordered sets 57R58: Floer homology

Keywords
Knot Floer homology shellable poset grid diagram flow category

Citation

Sarkar, Sucharit. Grid diagrams and shellability. Homology Homotopy Appl. 14 (2012), no. 2, 77--90. https://projecteuclid.org/euclid.hha/1355321481


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