On decrit la construction d'une famille particuliere de 4-varietes hyper-Kahler: les espaces asymptotiquement localement euclidiens ALE. On decrit une 4-variete de Riemann avec juste une extremite… Expand

1. Statement of the result The genus of a smooth algebraic curve of degree d in CP is given by the formula g = (d − 1)(d − 2)/2. A conjecture sometimes attributed to Thom states that the genus of the… Expand

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… Expand

We prove that a knot is the unknot if and only if its reduced Khovanov cohomology has rank 1. The proof has two steps. We show first that there is a spectral sequence beginning with the reduced… Expand

We develop monopole and instanton Floer homology groups for balanced sutured manifolds, in the spirit of [12]. Applications include a new proof of Property P for knots.