Knot Floer homology and the four-ball genus

@inproceedings{Ozsvth2003KnotFH,
  title={Knot Floer homology and the four-ball genus},
  author={Peter S. Ozsv{\'a}th and Zolt{\'a}n Szab{\'o}},
  year={2003}
}
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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