Abstract
We use the knot filtration on the Heegaard Floer complex to define an integer invariant 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 also the 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.
Citation
Peter Ozsváth. Zoltán Szabó. "Knot Floer homology and the four-ball genus." Geom. Topol. 7 (2) 615 - 639, 2003. https://doi.org/10.2140/gt.2003.7.615
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