Algebraic & Geometric Topology

Grid diagrams and Manolescu's unoriented skein exact triangle for knot Floer homology

Michael Wong

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Abstract

We rederive Manolescu’s unoriented skein exact triangle for knot Floer homology over F2 combinatorially using grid diagrams, and extend it to the case with  coefficients by sign refinements. Iteration of the triangle gives a cube of resolutions that converges to the knot Floer homology of an oriented link. Finally, we reestablish the homological σ–thinness of quasialternating links.

Article information

Source
Algebr. Geom. Topol., Volume 17, Number 3 (2017), 1283-1321.

Dates
Received: 26 May 2013
Revised: 9 September 2016
Accepted: 5 January 2017
First available in Project Euclid: 16 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1510841399

Digital Object Identifier
doi:10.2140/agt.2017.17.1283

Mathematical Reviews number (MathSciNet)
MR3677929

Zentralblatt MATH identifier
1373.57051

Subjects
Primary: 57R58: Floer homology
Secondary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45} 57M27: Invariants of knots and 3-manifolds

Keywords
knot Floer homology grid diagrams grid homology unoriented skein

Citation

Wong, Michael. Grid diagrams and Manolescu's unoriented skein exact triangle for knot Floer homology. Algebr. Geom. Topol. 17 (2017), no. 3, 1283--1321. doi:10.2140/agt.2017.17.1283. https://projecteuclid.org/euclid.agt/1510841399


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