#### Volume 17, issue 3 (2017)

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

### C-M Michael Wong

Algebraic & Geometric Topology 17 (2017) 1283–1321
##### Abstract

We rederive Manolescu’s unoriented skein exact triangle for knot Floer homology over ${\mathbb{F}}_{2}$ combinatorially using grid diagrams, and extend it to the case with $ℤ$ 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 $\sigma$–thinness of quasialternating links.

##### Keywords
knot Floer homology, grid diagrams, grid homology, unoriented skein
##### Mathematical Subject Classification 2010
Primary: 57R58
Secondary: 57M25, 57M27