Property P conjecture
In mathematics, the Property P conjecture is a statement about 3-manifolds obtained by Dehn surgery on a knot in the 3-sphere. A knot in the 3-sphere is said to have Property P if every 3-manifold obtained by performing (non-trivial) Dehn surgery on the knot is non-simply-connected. The conjecture states that all knots, except the unknot, have Property P.
Research on Property P was jump-started by R. H. Bing, who popularized the name and conjecture.
A proof was announced in 2004, as the combined result of efforts of mathematicians working in several different fields.
- Eliashberg, Yakov (2004). "A few remarks about symplectic filling". Geometry & Topology. 8: 277–293. arXiv: . doi:10.2140/gt.2004.8.277.
- Etnyre, John B. (2004). "On symplectic fillings". Algebraic & Geometric Topology. 4: 73–80. arXiv: . doi:10.2140/agt.2004.4.73.
- Kronheimer, Peter; Mrowka, Tomasz (2004). "Witten's conjecture and Property P". Geometry & Topology. 8: 295–310. arXiv: . doi:10.2140/gt.2004.8.295.
- Ozsvath, Peter; Szabó, Zoltán (2004). "Holomorphic disks and genus bounds". Geometry & Topology. 8: 311–334. arXiv: . doi:10.2140/gt.2004.8.311.
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