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Lens space surgeries and tunnel number one knots


Speaker: Mike Williams, UC Davis
Location: 2112 MSB
Start time: Wed, Nov 7 2007, 4:10PM

In the 1990's John Berge showed that a certain class of tunnel number one knots in the 3-sphere, called double primitive knots, admit lens space surgeries. Then Cameron Gordon conjectured that if a knot in the 3-sphere admits a lens space surgery, then that knot is double primitive. I will discuss an approach to prove this conjecture for all tunnel number one knots in terms of genus 2 Heegaard splittings. With this approach, there are three cases. I will discuss the proof in two of the cases.