Berge conjecture
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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.
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