Algebraic & Geometric Topology

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

Michael Wong

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

knot Floer homology grid diagrams grid homology unoriented skein


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.

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