706 research outputs found
The big Dehn surgery graph and the link of S^3
In a talk at the Cornell Topology Festival in 2005, W. Thurston discussed a
graph which we call "The Big Dehn Surgery Graph", B. Here we explore this
graph, particularly the link of S^3, and prove facts about the geometry and
topology of B. We also investigate some interesting subgraphs and pose what we
believe are important questions about B.Comment: 15 pages, 4 figures, 4 ancillary files. Reorganized and shortened
from previous versions, while correcting one error in the proof of Theorem
5.4. Also, ancillary files detailing our computations with the computer
program ORB have been provide
Commensurability classes containing three knot complements
This paper exhibits an infinite family of hyperbolic knot complements that have three knot complements in their respective commensurability classes.Mathematic
On knot complements that decompose into regular ideal dodecahedra
Aitchison and Rubinstein constructed two knot complements that can be decomposed into two regular ideal dodecahedra. This paper shows that these knot complements are the only knot complements that decompose into n regular ideal dodecahedra, providing a partial solution to a conjecture of Neumann and Reid.Mathematic
Small knot complements, exceptional surgeries, and hidden symmetries
This paper provides two obstructions to small knot complements in S3 admitting hidden symmetries. The first obstruction is being cyclically commensurable with another knot complement. This result provides a partial answer to a conjecture of Boileau, Boyer, Cebanu and Walsh. We also provide a second obstruction to admitting hidden symmetries in the case where a small knot complement covers a manifold admitting some symmetry and at least two exceptional surgeries.Mathematic
On manifolds with multiple lens space filings
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 and 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.Comment: 30 pages, 13 figure
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