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- Influence
Monopoles and Three-Manifolds
- P. Kronheimer, T. Mrowka
- Mathematics
- 21 January 2008
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
The Genus of Embedded Surfaces in the Projective Plane
- P. Kronheimer, T. Mrowka
- Mathematics
- 1994
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
Embedded surfaces and the structure of Donaldson's polynomial invariants
- P. Kronheimer, T. Mrowka
- Mathematics
- 1995
Knots, sutures, and excision
- P. Kronheimer, T. Mrowka
- Mathematics
- 30 July 2008
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.
Khovanov homology is an unknot-detector
- P. Kronheimer, T. Mrowka
- Mathematics
- 24 May 2010
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
Monopoles and lens space surgeries
- P. Kronheimer, T. Mrowka, P. Ozsv'ath, Z. Szabó
- Mathematics
- 13 October 2003
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
Gauge theory for embedded surfaces, II
- P. Kronheimer, T. Mrowka
- Mathematics
- 1 October 1993
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
Witten's conjecture and Property P
- P. Kronheimer, T. Mrowka
- Mathematics
- 27 November 2003
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