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On knot Floer width and Turaev genus
Adam 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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