On knot Floer width and Turaev genus

By Adam M. Lowrance. 2007

56 citations recorded by the source corpus.

To each knot $K\subset S^3$ one can associated its knot Floer homology $\hat{HFK}(K)$, 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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8bc704694e533e966675faf81bd498056608a2fb

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In Geometry and Topology

1. John A. Baldwin
2. Ilya Kofman
3. Abhijit Champanerkar
4. W. D. Gillam
5. J. Greene
6. Lawrence P. Roberts
7. Peter S. Ozsv'ath
8. Zolt'an Szab'o

In Mathematical Physics

1. John A. Baldwin
2. Ilya Kofman
3. Abhijit Champanerkar
4. W. D. Gillam
5. Lawrence P. Roberts

Citations in the corpus

• Computations of Heegaard-Floer knot homology (2006, background): “width and Turaev genus [15], and by Greene to prove the existence of homologically”
• Twisting quasi-alternating links (2007, background): “Khovanov homology and knot Floer homology [16, 5, 13 ].”