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- Nathan Broaddus, Walter Neumann, +4 authors Brian Mangum
- 2004

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)

- Nathan Broaddus
- 2007

Harer has shown that the mapping class group is a virtual duality groupmirroring the work of Borel-Serre on arithmetic groups in semisimple Q-groups. Just as the homology of the rational Tits building provides the dualizing module for any torsion-free arithmetic group, the homology of the curve complex is the dualizingmodule for any torsion-free, finite… (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)

We bound the value of the Casson invariant of any integral homology 3-sphere M by a constant times the distance-squared to the identity, measured in any word metric on the Torelli group I, of the element of I associated to any Heegaard splitting of M . We construct examples which show this bound is asymptotically sharp.

- Joan S. Birman, Tara E. Brendleand, Nathan Broaddus
- 2007

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)

- Joan Birman, Nathan Broaddus, William Menasco
- 2014

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)

- Travis P Wagner, Nathan Broaddus
- Waste management
- 2016

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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