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 lens space surgery, then it is fibered. Berge knots are fibered.

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

References

• Yi Ni. Knot Floer homology detects fibred knots. Invent. Math. 170 (2007), no. 3, 577–608.
• Yi Ni. Corrigendum to: Knot Floer homology detects fibred knots (pdf)

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