On knot Floer width and Turaev genus

Lowrance, Adam

doi:10.2140/agt.2008.8.1141

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On knot Floer width and Turaev genus

Adam M Lowrance

Algebraic & Geometric Topology 8 (2008) 1141–1162

DOI: 10.2140/agt.2008.8.1141

Abstract

To each knot $K \subset S^{3}$ one can associate with its knot Floer homology $\hat{H F K} (K)$ , 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.

Keywords

knot, Floer, Turaev genus, graphs on surfaces, ribbon graph, width

Mathematical Subject Classification 2000

Primary: 57R58, 57M25

References

Publication

Received: 12 October 2007

Revised: 5 March 2008

Accepted: 25 March 2008

Published: 25 July 2008

Authors

Adam M Lowrance
Department of Mathematics Louisiana State University Baton Rouge LA 70803 USA
http://www.math.lsu.edu/~lowrance

Volume 8, issue 2 (2008)