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

Wong, Michael

doi:10.2140/agt.2017.17.1283

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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

DOI: 10.2140/agt.2017.17.1283

Abstract

We rederive Manolescu’s unoriented skein exact triangle for knot Floer homology over $F_{2}$ 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 $σ$ –thinness of quasialternating links.

Keywords

knot Floer homology, grid diagrams, grid homology, unoriented skein

Mathematical Subject Classification 2010

Primary: 57R58

Secondary: 57M25, 57M27

References

Publication

Received: 26 May 2013

Revised: 9 September 2016

Accepted: 5 January 2017

Published: 17 July 2017

Authors

C-M Michael Wong
Department of Mathematics Columbia University New York, NY 10027 United States
http://www.math.columbia.edu/~cmmwong

Volume 17, issue 3 (2017)