Portal de Periódicos da CAPES

Monopoles and lens space surgeries

2003; Cornell University; Linguagem: Inglês

10.48550/arxiv.math/0310164

P. B. Kronheimer, Tomasz Mrowka, Peter Ozsváth, Zoltán Szabó,

Advanced Operator Algebra Research

Monopole Floer homology is used to prove that real projective three-space cannot be obtained from Dehn surgery on a non-trivial knot in the three-sphere. To obtain this result, we use a surgery long exact sequence for monopole Floer homology, together with a non-vanishing 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.