On manifolds with multiple lens space filings

Abstract

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 $S^3$ and $S^1\times S^2$ 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.

30 pages, 13 figures

References in corpus (5)

• Lens space surgeries and L-space homology spheres
• Grid Diagrams for Lens Spaces and Combinatorial Knot Floer Homology
• Bridge number and integral Dehn surgery
• Some knots in S^1 x S^2 with lens space surgeries
• Lens space surgeries along certain 2-component links related with Park's rational blow down, and Reidemeister-Turaev torsion