Berge conjecture

Berge conjecture

In the mathematical subject of knot theory, the Berge conjecture states that the only knots in the 3-sphere which admit lens space surgeries are Berge knots. The conjecture (and family of Berge knots) is named after John Berge.

Progress on the conjecture has been slow. Recently Yi Ni proved that if a knot admits a len space surgeries, then it is fibered. Berge knots are fibered.


Wikimedia Foundation. 2010.

Игры ⚽ Поможем написать реферат

Look at other dictionaries:

  • Berge knot — In the mathematical theory of knots, a Berge knot or doubly primitive knot is any member of a particular family of knots in the 3 sphere. A Berge knot K is defined by the conditions: # K lies on a genus two Heegaard surface S # in each handlebody …   Wikipedia

  • List of mathematics articles (B) — NOTOC B B spline B* algebra B* search algorithm B,C,K,W system BA model Ba space Babuška Lax Milgram theorem Baby Monster group Baby step giant step Babylonian mathematics Babylonian numerals Bach tensor Bach s algorithm Bachmann–Howard ordinal… …   Wikipedia

  • List of knot theory topics — Knot theory is the study of mathematical knots. While inspired by knots which appear in daily life in shoelaces and rope, a mathematician s knot differs in that the ends are joined together so that it cannot be undone. In precise mathematical… …   Wikipedia

  • Distance-hereditary graph — A distance hereditary graph. In graph theoretic mathematics, a distance hereditary graph (also called a completely separable graph)[1] is a graph in which the distances in any connected induced subgraph are the same as they are in the original… …   Wikipedia

  • Coloration De Graphe — En mathématiques, la coloration de graphe renvoie à un champ d études appartenant à la théorie des graphes. Il s agit de déterminer combien de couleurs différentes suffisent pour colorer entièrement un graphe de telle façon qu aucun nœud du… …   Wikipédia en Français

  • Nombre chromatique — Coloration de graphe En mathématiques, la coloration de graphe renvoie à un champ d études appartenant à la théorie des graphes. Il s agit de déterminer combien de couleurs différentes suffisent pour colorer entièrement un graphe de telle façon… …   Wikipédia en Français

  • Theoreme quatre couleurs — Coloration de graphe En mathématiques, la coloration de graphe renvoie à un champ d études appartenant à la théorie des graphes. Il s agit de déterminer combien de couleurs différentes suffisent pour colorer entièrement un graphe de telle façon… …   Wikipédia en Français

  • combinatorics — /keuhm buy neuh tawr iks, tor , kom beuh /, n. (used with singular v.) See combinatorial analysis. * * * Branch of mathematics concerned with the selection, arrangement, and combination of objects chosen from a finite set. The number of possible… …   Universalium

  • Perfect graph — The Paley graph of order 9, colored with three colors and showing a clique of three vertices. In this graph and each of its induced subgraphs the chromatic number equals the clique number, so it is a perfect graph. In graph theory, a perfect… …   Wikipedia

  • Théorème des graphes parfaits — Le graphe parfait est une notion introduite par Claude Berge, dont les conjectures ont été démontrées en 1972 et 2002 et sont devenues des théorèmes. Sommaire 1 Contexte 2 Théorèmes 3 Intérêt …   Wikipédia en Français

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”