Knot Floer homology detects fibred knots

• 成果类型: Article
• 署名作者: Ni, Yi
• 署名单位: Princeton University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-007-0075-9
• 发表日期: 2007
• 页码: 577-608
• 关键词: HOLOMORPHIC DISKS; foliations; TOPOLOGY

摘要

Ozsvath and Szabo conjectured that knot Floer homology detects fibred knots in S-3. 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 (HFK) over cap (Y, K) is monic, then K is fibred. The proof relies on previous works due to Gabai, Ozsvath-Szabo, Ghiggini and the author. A corollary is that if a knot in S-3 admits a lens space surgery, then the knot is fibred.