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- Ruth Charney
- 2007

Recently, right-angled Artin groups have attracted much attention in geometric group theory. They have a rich structure of subgroups and nice algorithmic properties, and they give rise to cubical complexes with a variety of applications. This survey article is meant to introduce readers to these groups and to give an overview of the relevant literature.… (More)

- Ruth Charney, John Crisp, Karen Vogtmann
- 2007

Associated to any simplicial graph Γ is a right-angled Artin group AΓ. This class of groups includes free groups and free abelian groups and may be said to interpolate between these two extremes. We study the outer automorphism group of a right-angled Artin group in the case where the defining graph is connected and triangle-free. We give an algebraic… (More)

A Garside group is a group admitting a finite lattice generating set D. Using techniques developed by Bestvina for Artin groups of finite type, we construct K(π, 1)s for Garside groups. This construction shows that the (co)homology of any Garside group G is easily computed given the lattice D, and there is a simple sufficient condition that implies G is a… (More)

- Ruth Charney, John Crisp
- 2005

We observe that, for fixed n ≥ 3, each of the Artin groups of finite type An, Bn = Cn, and affine type An−1 and Cn−1 is a central extension of a finite index subgroup of the mapping class group of the (n + 2)-punctured sphere. (The centre is trivial in the affine case and infinite cyclic in the finite type cases). Using results of Ivanov and Korkmaz on… (More)

The paper addresses the problem of synthesizing programs using a restricted set of input-output data. The program to be synthesized consists of assigning to individual Boolean variables x , the result of evaluating functions involving other Boolean variables x. The program can be initially viewed as a black box having n inputs corresponding to the variables… (More)

- Rebecca S Torrey, Avner Ash, Kevin Buzzard, John Cremona, David Dummit, Frazer Jarvis +14 others
- 2009

Declaration This thesis is a presentation of my own original research work. Wherever contributions of others are involved, every effort has been made to indicate this clearly with due reference to the literature. Abstract In this thesis, I investigate a generalization to imaginary quadratic fields of the refined version of Serre's conjecture. I ask whether… (More)

- Ira M Gessel, T Kyle Petersen, Adam Jaffe, Ruth Charney, Richard Stanley
- 2006

Dedication To my love. iii Acknowledgments This document being, primarily, a mathematical effort, I must first thank those who influenced this work mathematically. Thanks to my advisor, Ira Gessel. Many of the main theorems regarding descents were his ideas, and I'm sure if he had wanted to take the time, he could have produced proofs of all the theorems I… (More)

- Ruth Charney, John Crisp
- 2006

This paper considers the question of relative hyperbolicity of an Artin group with regard to the geometry of its associated Deligne complex. We prove that an Artin group is weakly hyperbolic relative to its finite (or spherical) type parabolic subgroups if and only if its Deligne complex is a Gromov hyperbolic space. For a 2-dimensional Artin group the… (More)

- Ruth Charney
- IJAC
- 2000

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