Milnor conjecture (topology)

For Milnor's conjecture about K-theory, see Milnor conjecture.

In knot theory, the Milnor conjecture says that the slice genus of the (p,q) torus knot is

(p − 1)(q − 1) / 2.

It is in a similar vein to the Thom conjecture.

It was first proved by gauge theoretic methods by Peter Kronheimer and Tomasz Mrowka.^[1] Jacob Rasmussen later gave a purely combinatorial proof using Khovanov homology, by means of the s-invariant.^[2]

References

1. ^ Kronheimer, P. B.; Mrowka, T. S. (1993), "Gauge theory for embedded surfaces, I", Topology 32 (4): 773–826, doi:10.1016/0040-9383(93)90051-V .
2. ^ Rasmussen, Jacob A. (2004). "Khovanov homology and the slice genus". arXiv:math.GT/0402131. .

This topology-related article is a stub. You can help Wikipedia by expanding it.v · Categories: Geometric topology Knot theory 4-manifolds Conjectures Topology stubs Wikimedia Foundation. 2010. Игры ⚽ Нужна курсовая? Dr. David Cameron Tawny-breasted Parrotfinch Look at other dictionaries: Milnor conjecture — For Milnor s conjecture about the slice genus of torus knots, see Milnor conjecture (topology). In mathematics, the Milnor conjecture was a proposal by John Milnor (1970) of a description of the Milnor K theory (mod 2) of a general… …   Wikipedia Conjecture de Milnor (théorie des nœuds) —  Pour la conjecture de Milnor en K théorie algébrique (en), voir Conjecture de Milnor.  En théorie des nœuds, la conjecture de Milnor affirme que le 4 genre  …   Wikipédia en Français Conjecture de Milnor —  Pour l’article homonyme, voir Conjecture de Milnor (théorie des nœuds).  En mathématiques, la conjecture de Milnor dit que pour tout corps F de caractéristique différente de 2, la K théorie de Milnor (en) …   Wikipédia en Français Conjecture de géométrisation — En mathématiques, et plus précisément en géométrie, la conjecture de géométrisation de Thurston affirme que les variétés compactes de dimension 3 peuvent être décomposées en sous variétés admettant l une des huit structures géométriques appelées… …   Wikipédia en Français Milnor, John Willard — ▪ American mathematician born February 20, 1931, Orange, New Jersey, U.S.       American mathematician who was awarded the Fields Medal in 1962 for his work in differential topology.       Milnor attended Princeton University (A.B., 1951; Ph.D.,… …   Universalium John Milnor — For those of a similar name, see John Milner (disambiguation). John Willard Milnor Born February 20, 1931 ( …   Wikipedia John Milnor — John Willard Milnor, né le 20 février 1931, est un mathématicien connu pour son travail en topologie différentielle et en K théorie. Sommaire 1 Biographie …   Wikipédia en Français Poincaré conjecture — In mathematics, the Poincaré conjecture (French, pronounced|pwɛ̃kaʀe) [cite encyclopedia | encyclopedia=The American Heritage Dictionary of the English Language | title=Poincaré, Jules Henri | url=http://www.bartleby.com/61/3/P0400300.html |… …   Wikipedia Generalized Poincaré conjecture — In the mathematical area of topology, the term Generalized Poincaré conjecture refers to a statement that a manifold which is a homotopy sphere is a sphere. More precisely, one fixes a category of manifolds: topological (Top), differentiable… …   Wikipedia Novikov conjecture — This page concerns mathematician Sergei Novikov s topology conjecture. For astrophysicist Igor Novikov s conjecture regarding time travel, see Novikov self consistency principle. The Novikov conjecture is one of the most important unsolved… …   Wikipedia 18+ © Academic, 2000-2024 Contact us: Technical Support, Advertising Dictionaries export, created on PHP, Joomla, Drupal, WordPress, MODx. Mark and share Search through all dictionaries Translate… Search Internet Share the article and excerpts Direct link … Do a right-click on the link above and select “Copy Link”