Knot Floer homology and the four-ball genus

  title={Knot Floer homology and the four-ball genus},
  author={Peter S. Ozsv{\'a}th and Zolt{\'a}n Szab{\'o}},
We use the knot filtration on the Heegaard Floer complex CF to define an integer for knots. Like the classical signature, this invariant gives a homomorphism from the knot concordance group to . As such, it gives lower bounds for the slice genus (and hence unknotting number) of a knot; but unlike the signature, gives sharp bounds on the four-ball genera of torus knots. As another illustration, we calculate the invariant for several ten-crossing knots. 
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Publications referenced by this paper.
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Z Szabó

PS Ozsváth
Holomorphic disks and knot invariants • 2002
View 19 Excerpts
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Heegaard Floer homology and alternating knots

Peter Ozsv, ath Zolt
View 7 Excerpts
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Peter Ozsv´ath, Zolt´an Szab´o
View 3 Excerpts
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Knot Floer homology

PS Ozsváth, Z Szabó
genus bounds, and mutation • 2003
View 5 Excerpts
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Floer homologies of surgeries on two - bridge knots , Algebr

Z Szabó P S Ozsváth
Geom . Topol . • 2003

S Strle

B Owens
Rational homology spheres and four-ball genus • 2003

Singular points of complex hypersurfaces

JW Milnor
Annals of Mathematics Studies 61, Princeton University Press (1968) Geometry & Topology, Volume 7 • 2003

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