  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.
