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Lens space surgeries and primitive/Seifert constructions
Student-Run Geometry/Topology Seminar| Speaker: | Michael Williams, UCD |
| Location: | 2112 MSB |
| Start time: | Thu, Apr 26 2007, 11:00AM |
An open problem in knot theory is to determine which knots in the 3-sphere admit lens space Dehn surgeries. A natural way to produce lens space surgeries is the primitive/primitive construction due to John Berge. It is conjectured that any lens space surgery arises from this construction. A more general construction is the primitive/Seifert construction due to John Dean, and it generically produces Seifert-fibered surgeries. Mario Eudave-Mu\~noz has given examples of primitive/Seifert constructions which yield lens space surgeries; in these examples, the surgeries also arise from a primitive/primitive construction. I will present a proof that, in general, if a primitve/Seifert construction yields a lens space surgery, then the surgery also arises from a primitive/primitive construction.