Knot Floer homology and the four-ball genus

Research output: Contribution to journalArticle

200 Scopus citations

Abstract

We use the knot filtration on the Heegaard Floer complex CF to define an integer invariant τ(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, τ gives sharp bounds on the four-ball genera of torus knots. As another illustration, we calculate the invariant for several ten-crossing knots.

Original languageEnglish (US)
Pages (from-to)615-639
Number of pages25
JournalGeometry and Topology
Volume7
DOIs
StatePublished - 2003

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

Keywords

  • 4-ball genus
  • Floer homology
  • Knot concordance
  • Signature

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