Monopoles and lens space surgeries

P. Kronheimer, T. Mrowka, P. Ozsváth, Z. Szabó

Research output: Contribution to journalArticlepeer-review

126 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)457-546
Number of pages90
JournalAnnals of Mathematics
Volume165
Issue number2
DOIs
StatePublished - Mar 2007

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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