To install click the Add extension button. That's it.

The source code for the WIKI 2 extension is being checked by specialists of the Mozilla Foundation, Google, and Apple. You could also do it yourself at any point in time.

Kelly Slayton
Congratulations on this excellent venture… what a great idea!
Alexander Grigorievskiy
I use WIKI 2 every day and almost forgot how the original Wikipedia looks like.
Live Statistics
English Articles
Improved in 24 Hours
Added in 24 Hours
What we do. Every page goes through several hundred of perfecting techniques; in live mode. Quite the same Wikipedia. Just better.

From Wikipedia, the free encyclopedia

In the mathematical theory of knots, a Berge knot (named after mathematician John Berge) 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:

  1. K lies on a genus two Heegaard surface S
  2. in each handlebody bound by S, K meets some meridian disc exactly once.

John Berge constructed these knots as a way of creating knots with lens space surgeries and classified all the Berge knots. Cameron Gordon conjectured these were the only knots admitting lens space surgeries. This is now known as the Berge conjecture.

YouTube Encyclopedic

  • 1/3
    116 760
    718 770
    13 141
  • AlgTop0: Introduction to Algebraic Topology
  • 3 Surprising Things Matter Does Under Extreme Pressure
  • AlgTopReview4: Free abelian groups and non-commutative groups



Berge conjecture

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 lens space surgery, then it is fibered. Subsequently, Joshua Greene showed that the lens spaces which are realized by surgery on a knot in the 3-sphere are precisely the lens spaces arising from surgery along the Berge knots.

Further reading


  • Baker, Kenneth L. (2008), "Surgery descriptions and volumes of Berge knots. I. Large volume Berge knots", Journal of Knot Theory and its Ramifications, 17 (9): 1077–1097, arXiv:math/0509054, doi:10.1142/S0218216508006518, MR 2457837.
  • Baker, Kenneth L. (2008), "Surgery descriptions and volumes of Berge knots. II. Descriptions on the minimally twisted five chain link", Journal of Knot Theory and its Ramifications, 17 (9): 1099–1120, arXiv:math/0509055, doi:10.1142/S021821650800652X, MR 2457838.
  • Yamada, Yuichi (2005), "Berge's knots in the fiber surfaces of genus one, lens space and framed links", Journal of Knot Theory and its Ramifications, 14 (2): 177–188, doi:10.1142/S0218216505003774, MR 2128509.


External links

Two blog posts in the weblog "Low Dimensional Topology - Recent Progress and Open Problems" related to the Berge conjecture:

The Berge conjecture, by Jesse Johnson
Knot complements covering knot complements by Ken Baker
This page was last edited on 6 October 2018, at 05:11
Basis of this page is in Wikipedia. Text is available under the CC BY-SA 3.0 Unported License. Non-text media are available under their specified licenses. Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc. WIKI 2 is an independent company and has no affiliation with Wikimedia Foundation.