Monopoles and lens space surgeries

• 成果类型: Article
• 署名作者: Kronheimer, P.; Mrowka, T.; Ozsvath, P.; Szabo, Z.
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2007.165.457
• 发表日期: 2007
• 页码: 457-546
• 关键词: punctured surface bundles; holomorphic disks; FLOER HOMOLOGY; dehn surgery; reebless foliation; instanton homology; TAUT FOLIATIONS; cyclic surgery; KNOTS; 3-manifolds

摘要

Monopole Floer homology is used to prove that real projective three-space cannot be obtained from Dehn surgery on a nontrivial knot in the three-sphere. To obtain this result, we use a surgery long exact sequence for monopole Floer homology, together with a nonvanishing theorem, which shows that monopole Floer homology detects the unknot. In addition, we apply these techniques to give information about knots which admit lens space surgeries, and to exhibit families of three-manifolds which do not admit taut foliations.