Browsing by Subject "math.GT: Geometric Topology"

Now showing items 1-15 of 15

    • Big Dehn surgery graph and the link of s^3 

      Hoffman, Neil R.; Walsh, Genevieve S. (2013-11-15)

    • Commensurability classes containing three knot complements 

      Hoffman, Neil (2009-05-11)
      This paper exhibits an infinite family of hyperbolic knot complements that have three knot complements in their respective commensurability classes.

    • Cusp types of quotients of hyperbolic knot complements 

      Hoffman, Neil R. (2020-01-14)
      This paper completes a classification of the types of orientable and non-orientable cusps that can arise in the quotients of hyperbolic knot complements. In particular, S2(2,4,4) cannot be the cusp cross-section of any ...

    • Exceptional surgeries in 3-manifolds 

      Baker, Kenneth L.; Hoffman, Neil R. (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 ...

    • Infinitely many virtual geometric triangulations 

      Futer, David; Hamilton, Emily; Hoffman, Neil R. (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 ...

    • Jointly primitive knots and surgeries between lens spaces 

      Baker, Kenneth L.; Hoffman, Neil R.; Licata, Joan E. (2019-04-05)
      This paper describes a Dehn surgery approach to generating asymmetric hyperbolic manifolds with two distinct lens space fillings. Such manifolds were first identified in work of Dunfield-Hoffman-Licata as the result of a ...

    • Null-homologous exotic surfaces in 4-manifolds 

      Hoffman, Neil R.; Sunukjian, Nathan S. (2013-10-07)
      In this paper we exhibit infinite families of embedded tori in 4-manifolds that are topologically isotopic but smoothly distinct. The interesting thing about these tori is that they are topologically trivial in the sense ...

    • On knot complements that decompose into regular ideal dodecahedra 

      Hoffman, Neil (2012-09-05)
      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 ...

    • On manifolds with multiple lens space filings 

      Baker, Kenneth L.; Doleshal, Brandy Guntel; Hoffman, Neil (2013-08-22)
      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 ...

    • On the complexity of cusped non-hyperbolicity 

      Haraway, Robert, III; Hoffman, Neil R. (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 ...

    • Poincare homology sphere, lens space surgeries, and some knots with tunnel number two 

      Baker, Kenneth L.; Hoffman, Neil R. (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. ...

    • Small knot complements, exceptional surgeries, and hidden symmetries 

      Hoffman, Neil (2011-10-17)
      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 ...

    • Small PSL(2,F) representations of Seifert fiber space groups 

      Hoffman, Neil R.; Petersen, Kathleen L. (2022-09-12)
      Let M be a Seifert fiber space with non-abelian fundamental group and admitting a triangulation with t tetrahedra. We show that there is a non-abelian PSL(2,F) quotient where |F|<c(220t3120t) for an absolute constant c>0 ...

    • Symmetries and hidden symmetries of ε,dL-twisted knot complements 

      Hoffman, Neil R.; Millichap, Christian; Worden, William (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 ...

    • Verified computations for hyperbolic 3-manifolds 

      Hoffman, Neil; Ichihara, Kazuhiro; Kashiwagi, Masahide; Masai, Hidetoshi; Oishi, Shin'ichi; Takayasu, Akitoshi (2013-10-12)
      For a given cusped 3-manifold M admitting an ideal triangulation, we describe a method to rigorously prove that either M or a filling of M admits a complete hyperbolic structure via verified computer calculations. Central ...