Geodesic
On knot Floer width and Turaev genus
Lowrance, Adam1
1Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, USA
Algebraic and Geometric Topology, Tome 8 (2008) no. 2, pp. 1141-1162
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To each knot K ⊂ S3 one can associate with its knot Floer homology HFK̂(K), a finitely generated bigraded abelian group. In general, the nonzero ranks of these homology groups lie on a finite number of slope one lines with respect to the bigrading. The width of the homology is, in essence, the largest horizontal distance between two such lines. Also, for each diagram D of K there is an associated Turaev surface, and the Turaev genus is the minimum genus of all Turaev surfaces for K. We show that the width of knot Floer homology is bounded by Turaev genus plus one. Skein relations for genus of the Turaev surface and width of a complex that generates knot Floer homology are given.

DOI : 10.2140/agt.2008.8.1141
Keywords: knot, Floer, Turaev genus, graphs on surfaces, ribbon graph, width

Lowrance, Adam  1

1 Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, USA 
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Lowrance, Adam. On knot Floer width and Turaev genus. Algebraic and Geometric Topology, Tome 8 (2008) no. 2, pp. 1141-1162. doi: 10.2140/agt.2008.8.1141

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