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

Wong, Michael¹

¹Department of Mathematics, Columbia University, New York, NY 10027, United States

Algebraic and Geometric Topology, Tome 17 (2017) no. 3, pp. 1283-1321

Résumé

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 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 σ–thinness of quasialternating links.

Détail

DOI : 10.2140/agt.2017.17.1283

Classification : 57R58, 57M25, 57M27
Keywords: knot Floer homology, grid diagrams, grid homology, unoriented skein

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