Nathan Broaddus

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Hempel has shown that the fundamental groups of knot complements are residually finite. This implies that every nontrivial knot must have a finite-sheeted, noncyclic cover. We give an explicit bound, Φ(c), such that if K is a nontrivial knot in the three-sphere with a diagram with c crossings then the complement of K has a finite-sheeted, noncyclic cover(More)
We prove that various subgroups of the mapping class group Mod(Σ) of a surface Σ are at least exponentially distorted. Examples include the Torelli group (answering a question of Hamenstädt), the “point-pushing” and surface braid subgroups, and the Lagrangian subgroup. Our techniques include a method to compute lower bounds on distortion via representation(More)
Johnson has defined a surjective homomorphism from the Torelli subgroup of the mapping class group of the surface of genus g with one boundary component to ∧H , the third exterior product of the homology of the surface. Morita then extended Johnson’s homomorphism to a homomorphism from the entire mapping class group to 1 2 ∧ 3 H ⋊ Sp(H). This Johnson-Morita(More)
Aramayona and Leininger have provided a “finite rigid subset” X(Σ) of the curve complex C (Σ) of a surface Σ = Σg , characterized by the fact that any simplicial injection X(Σ) → C (Σ) is induced by a unique element of the mapping class group Mod(Σ). In this paper we prove that, in the case of the sphere with n ≥ 5 marked points, the reduced homology class(More)
This study examined the generation of litter, defined as spillage and uncollected residue, from a curbside collection system for residential recycling. The primary recycling containers used in the study were 18-gal (68 L), open-top bins. The study, conducted over a seven-week period, was comprised of both an urban and suburban area. Six litter(More)
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