Surgery on complicated fibered knots

Surgery on complicated fibered knots

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Abigail Thompson , UC Davis/IAS
Fine Hall 314

It is a classical result that any closed orientable 3-manifold can be obtained by surgery on a link L in the 3-sphere. The link L may have many components. This leads to some natural questions: which 3-manifolds can be obtained by surgery on a knot K, and on which knots? Conjecturally, only Berge knots have surgeries yielding a lens space. The pool of potential counter-examples to this conjecture is slowly diminishing. I’ll describe a geometric condition that yields a class of fibered knots that cannot have lens space surgeries.