On manifolds with multiple lens space filings
Date
2013-08-22Author
Baker, Kenneth L.
Doleshal, Brandy Guntel
Hoffman, Neil
Metadata
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An irreducible 3--manifold with torus boundary either is a Seifert fibered space or admits at most three lens space fillings according to the Cyclic Surgery Theorem. We examine the sharpness of this theorem by classifying the non-hyperbolic manifolds with more than one lens space filling, classifying the hyperbolic manifolds obtained by filling of the Minimally Twisted 5 Chain complement that have three lens space fillings, showing that the doubly primitive knots in S3 and S1×S2 have no unexpected extra lens space surgery, and showing that the Figure Eight Knot Sister Manifold is the only non-Seifert fibered manifold with a properly embedded essential once-punctured torus and three lens space fillings.
Citation
Baker, K.L., Doleshal, B.G., Hoffman, N. (2013). On manifolds with multiple lens space filings.