Monopoles and lens space surgeries

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.

Authors

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