Monopoles and lens space surgeries


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.


Peter Kronheimer

Department of Mathematics, Harvard University, Cambridge, MA 02138, United States

Tomasz Mrowka

Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, United States

Peter Ozsváth

Department of Mathematics, Columbia University, New York, NY 10027, United States

Zoltán Szabó

Department of Mathematics, Princeton University, Princeton, NJ 08544, United States