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On knot Floer width and Turaev genus
Adam M Lowrance
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Algebraic & Geometric Topology 8
(2008) 1141–1162
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Abstract
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To each knot K⊂ S3 one can associate
with its knot Floer homology 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.
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Keywords
knot, Floer, Turaev genus, graphs on
surfaces, ribbon graph, width
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Mathematical Subject Classification
Primary: 57M25, 57R58
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Publication
Received: 12 October 2007
Revised: 5 March 2008
Accepted: 25 March 2008
Published: 25 July 2008
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Authors
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