Knot Floer homology and the four-ball genus

• DOI: 10.2140/gt.2003.7.615
• Publication Date: 2005-06-15T15:44:57Z
• Authors: Peter Ozsváth; Zoltán Szabó
• Keywords: Floer Homology; Khovanov homology; Ball (mathematics)

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