期刊
GEOMETRY & TOPOLOGY
卷 7, 期 -, 页码 615-639出版社
GEOMETRY & TOPOLOGY PUBLICATIONS
DOI: 10.2140/gt.2003.7.615
关键词
Floer homology; knot concordance; signature; 4-ball genus
类别
We use the knot filtration on the Heegaard Floer complex CF 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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