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

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.

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

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

This paper is the second in a series of two, aimed at developing results about the topology of embedded surfaces Σ in a 4-manifold X using some new YangMills moduli spaces associated to such pairs… Expand

Let K be a non-trivial knot in the 3{sphere and let Y be the 3{manifold obtained by surgery on K with surgery-coecient 1. Using tools from gauge theory and symplectic topology, it is shown that the… Expand