Zobrazeno 1 - 10
of 44
pro vyhledávání: '"WALSH, GENEVIEVE S."'
Autor:
Chesebro, Eric, Chu, Michelle, DeBlois, Jason, Hoffman, Neil R., Mondal, Priyadip, Walsh, Genevieve S.
We introduce a class of cusped hyperbolic $3$-manifolds that we call mixed-platonic, composed of regular ideal hyperbolic polyhedra of more than one type, which includes certain previously-known examples. We establish basic facts about mixed-platonic
Externí odkaz:
http://arxiv.org/abs/2407.01708
Autor:
Groves, Daniel, Haïssinsky, Peter, Manning, Jason F., Osajda, Damian, Sisto, Alessandro, Walsh, Genevieve S.
Given a hyperbolic group $G$ and a maximal infinite cyclic subgroup $\langle g \rangle$, we define a drilling of $G$ along $g$, which is a relatively hyperbolic group pair $(\widehat{G}, P)$. This is inspired by the well-studied procedure of drilling
Externí odkaz:
http://arxiv.org/abs/2406.14667
In this article, we prove a version of Martin and Skora's conjecture that convergence groups on the $2$-sphere are covered by Kleinian groups. Given a relatively hyperbolic group pair $(G,\mathcal{P})$ with planar boundary and no Sierpinski carpet or
Externí odkaz:
http://arxiv.org/abs/2405.20428
The aim of these notes is to connect the theory of hyperbolic and relatively hyperbolic groups to the theory of manifolds and Kleinian groups. We survey some of the extensive work that has been done in the field, and explain many examples. These note
Externí odkaz:
http://arxiv.org/abs/2201.12443
Publikováno v:
In Journal of Algebra 1 August 2024 651:1-18
We study the Bowditch boundaries of relatively hyperbolic group pairs, focusing on the case where there are no cut points. We show that if $(G,\mathcal{P})$ is a rigid relatively hyperbolic group pair whose boundary embeds in $S^2$, then the action o
Externí odkaz:
http://arxiv.org/abs/2008.07639
Autor:
Kim, Sang-hyun, Walsh, Genevieve S.
In this expository note, we illustrate phenomena and conjectures about boundaries of hyperbolic groups by considering the special cases of certain amalgams of hyperbolic groups. While doing so, we describe fundamental results on hyperbolic groups and
Externí odkaz:
http://arxiv.org/abs/1907.06898
Publikováno v:
Annales de la Facult\'e des Sciences de Toulouse Vol. 6 (2015) no.5 1179--1201
In this article we examine the conjecture of Neumann and Reid that the only hyperbolic knots in the $3$-sphere which admit hidden symmetries are the figure-eight knot and the two dodecahedral knots. Knots whose complements cover hyperbolic reflection
Externí odkaz:
http://arxiv.org/abs/1501.02253
Autor:
Hoffman, Neil R., Walsh, Genevieve S.
Publikováno v:
Proceedings of the American Mathematical Society, Series B . Vol. 2 (2015) 17--34
In a talk at the Cornell Topology Festival in 2005, W. Thurston discussed a graph which we call "The Big Dehn Surgery Graph", B. Here we explore this graph, particularly the link of S^3, and prove facts about the geometry and topology of B. We also i
Externí odkaz:
http://arxiv.org/abs/1311.3980
Autor:
Kim, Sang-hyun, Walsh, Genevieve S.
Publikováno v:
Journal of Topology Vol. 9 (2016) 117--142
Let $C(L)$ be the right-angled Coxeter group defined by an abstract triangulation $L$ of $\mathbb{S}^2$. We show that $C(L)$ is isomorphic to a hyperbolic right-angled reflection group if and only if $L$ can be realized as an acute triangulation. The
Externí odkaz:
http://arxiv.org/abs/1306.6025