• Publications
  • Influence
Monopoles and Three-Manifolds
Preface 1. Outlines 2. The Seiberg-Witten equations and compactness 3. Hilbert manifolds and perturbations 4. Moduli spaces and transversality 5. Compactness and gluing 6. Floer homology 7.Expand
  • 296
  • 66
  • PDF
The Genus of Embedded Surfaces in the Projective Plane
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 theExpand
  • 473
  • 39
  • PDF
Monopoles and contact structures
  • 166
  • 26
  • PDF
Knots, sutures, and excision
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.
  • 103
  • 22
  • PDF
Khovanov homology is an unknot-detector
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 reducedExpand
  • 197
  • 21
  • PDF
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 longExpand
  • 221
  • 21
  • PDF
Gauge theory for embedded surfaces, II
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 pairsExpand
  • 295
  • 18
  • PDF
Witten's conjecture and Property P
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 theExpand
  • 112
  • 12
  • PDF