Inventiones mathematicae

, Volume 170, Issue 3, pp 577–608

Knot Floer homology detects fibred knots

Authors

    • Department of MathematicsPrinceton University
Article

DOI: 10.1007/s00222-007-0075-9

Cite this article as:
Ni, Y. Invent. math. (2007) 170: 577. doi:10.1007/s00222-007-0075-9

Abstract

Ozsváth and Szabó conjectured that knot Floer homology detects fibred knots in S3. We will prove this conjecture for null-homologous knots in arbitrary closed 3-manifolds. Namely, if K is a knot in a closed 3-manifold Y, Y-K is irreducible, and \(\widehat{HFK}(Y,K)\) is monic, then K is fibred. The proof relies on previous works due to Gabai, Ozsváth–Szabó, Ghiggini and the author. A corollary is that if a knot in S3 admits a lens space surgery, then the knot is fibred.

Copyright information

© Springer-Verlag 2007