The lens space realization problem

• 成果类型: Article
• 署名作者: Greene, Joshua Evan
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2013.177.2.3
• 发表日期: 2013
• 页码: 449-511
• 关键词: knot floer homology; slice-ribbon conjecture; dehn surgeries; 4-manifolds

摘要

We determine the lens spaces that arise by integer Dehn surgery along a knot in the three-sphere. Specifically, if surgery along a knot produces a lens space, then there exists an equivalent surgery along a Berge knot with the same knot Floer homology groups. This leads to sharp information about the genus of such a knot. The arguments rely on tools from Floer homology and lattice theory. They are primarily combinatorial in nature.