Knot Floer homology and the four-ball genus
Geometric Topology
2014-11-11 v4 Symplectic Geometry
Abstract
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.
Keywords
Cite
@article{arxiv.math/0301149,
title = {Knot Floer homology and the four-ball genus},
author = {Peter Ozsvath and Zoltan Szabo},
journal= {arXiv preprint arXiv:math/0301149},
year = {2014}
}
Comments
Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol7/paper17.abs.html