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Big Dehn surgery graph and the link of s^3
(2013-11-15)
Infinitely many virtual geometric triangulations
(2021-02-24)
We prove that every cusped hyperbolic 3-manifold has a finite cover admitting infinitely many geometric ideal triangulations. Furthermore, every long Dehn filling of one cusp in this cover admits infinitely many geometric ...
Geometry of planar surfaces and exceptional fillings
(2015-04-07)
Poincare homology sphere, lens space surgeries, and some knots with tunnel number two
(2015-04-25)
We exhibit an infinite family of knots in the Poincare homology sphere with tunnel number 2 that have a lens space surgery. Notably, these knots are not doubly primitive and provide counterexamples to a few conjectures. ...
Exceptional surgeries in 3-manifolds
(2021-01-28)
Myers shows that every compact, connected, orientable 3--manifold with no 2--sphere boundary components contains a hyperbolic knot. We use work of Ikeda with an observation of Adams-Reid to show that every 3--manifold ...
Symmetries and hidden symmetries of ε,dL-twisted knot complements
(2019-09-23)
In this paper we analyze symmetries, hidden symmetries, and commensurability classes of (ϵ,dL)-twisted knot complements, which are the complements of knots that have a sufficiently large number of twists in each of their ...
Commensurability classes containing three knot complements
(2009-05-11)
This paper exhibits an infinite family of hyperbolic knot complements that have three knot complements in their respective commensurability classes.
On the complexity of cusped non-hyperbolicity
(2019-07-02)
We show that the problem of showing that a cusped 3-manifold M is not hyperbolic is in NP, assuming S3-RECOGNITION is in coNP. To this end, we show that IRREDUCIBLE TOROIDAL RECOGNITION lies in NP. Along the way we ...