Knot Floer homology and the four-ball genus

Ozsváth, Peter¹ ; Szabó, Zoltán²

¹ Department of Mathematics, Columbia University, New York 10025, USA
² Department of Mathematics, Princeton University, New Jersey 08540, USA

Geometry & topology, Tome 7 (2003) no. 2, pp. 615-639.

Résumé

We use the knot filtration on the Heegaard Floer complex $\widehat{CF}$ to define an integer invariant $\tau \left(K\right)$ for knots. Like the classical signature, this invariant gives a homomorphism from the knot concordance group to $\mathbb{Z}$. As such, it gives lower bounds for the slice genus (and hence also the unknotting number) of a knot; but unlike the signature, $\tau$ gives sharp bounds on the four-ball genera of torus knots. As another illustration, we calculate the invariant for several ten-crossing knots.

Détail

DOI : 10.2140/gt.2003.7.615

Keywords: Floer homology, knot concordance, signature, 4–ball genus

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