A combinatorial spanning tree model for knot Floer homology

By John A. Baldwin, A. Levine. 2011

52 citations recorded by the source corpus.

Abstract We iterate Manolescu’s unoriented skein exact triangle in knot Floer homology with coefficients in the field of rational functions over Z / 2 Z . The result is a spectral sequence which converges to a stabilized version of δ -graded knot Floer homology. The ( E 2 , d 2 ) page of this spectral sequence is an algorithmically computable chain complex expressed in terms of spanning trees, and we show that there are no higher differentials. This gives the first combinatorial spanning tree model for knot Floer homology.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7652bf313d221d6249855d936603b599adc427d6

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Citations in the corpus

Grid Homology for Knots and Links (2015, background): “More generally, Baldwin and Levine [6] conjecture an affirmative answer to the following question:”
On the geography and botany of knot Floer homology (2014, background): “2 Several combinatorial interpretations of this invariant now exist [8,53,54,70].”
Khovanov module and the detection of unlinks (2012, background): “Their result had numerous antecedents [1, 2, 3, 10, 11, 12, 13, 37], most aimed at generalizing or exploiting a spectral sequence discovered by Ozsváth and Szabó [31] which begins at Khovanov homology and converges to the Heegaard Floer homology of the branched double cover.”
AN INTRODUCTION TO KNOT FLOER HOMOLOGY (2014, unknown): “…(2) another by Sarkar and Wang, using nice diagrams [SW10]; (3) another by Ozsv´ath and Szab´o, using a cube of resolutions [OS09]; (4) another by Baldwin and Levine, in terms of spanning trees [BL12]; (5) yet another recently announced by Ozsv´ath and Szab´o, based on bordered Floer homology.”