Knot Floer homology and the four-ball genus

Details Knot Floer homology and the four-ball genus Knot Floer homology and the four-ball genus

2003-01-14

arxiv.org/abs/math/0301149v4

Geom. Topol. 7(2003) 615-639

Mathematics

Geometric Topology

Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol7/paper17.abs.html

Scientific paper

We use the knot filtration on the Heegaard Floer complex to define an integer invariant tau(K) for knots. Like the classical signature, this invariant gives a homomorphism from the knot concordance group to 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.

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