Rose Morris-Wright
YOU?
Author Swipe
View article: Rewriting in Artin groups without A_3 or B_3 subdiagrams
Rewriting in Artin groups without A_3 or B_3 subdiagrams Open
We prove that the word problem in an Artin group G based on a diagram without A_3 or B_3 subdiagrams can be solved using a system of length preserving rewrite rules which, together with free reduction, can be used to reduce any word over t…
View article: Acylindrical hyperbolicity for Artin groups with a visual splitting
Acylindrical hyperbolicity for Artin groups with a visual splitting Open
We establish a criterion that implies the acylindrical hyperbolicity of many Artin groups admitting a visual splitting. This gives a variety of new examples of acylindrically hyperbolic Artin groups, including many Artin groups of FC-type.…
View article: Pattern preserving quasi-isometries in lamplighter groups and other related groups
Pattern preserving quasi-isometries in lamplighter groups and other related groups Open
In this paper we explore the interplay between aspects of the geometry and algebra of three families of groups of the form B semidirect the integers Z, namely Lamplighter groups, solvable Baumslag-Solitar groups and lattices in SOL. In par…
View article: The Artin monoid Cayley graph
The Artin monoid Cayley graph Open
In this paper, we investigate properties of the Artin monoid Cayley graph. This is the Cayley graph of an Artin group A_{\Gamma} with respect to the (infinite) generating set given by the associated Artin monoid A^+_{\Gamma} . In a previou…
View article: The Artin monoid Cayley graph
The Artin monoid Cayley graph Open
In this paper we investigate properties of the Artin monoid Cayley graph. This is the Cayley graph of an Artin group $A_Γ$ with respect to the (infinite) generating set given by the associated Artin monoid $A^+_Γ$. In a previous paper, the…
View article: The Word Problem is Solvable for 3-free Artin groups in Quadratic Time
The Word Problem is Solvable for 3-free Artin groups in Quadratic Time Open
We give a quadratic-time explicit and computable algorithm to solve the word problem for Artin groups that do not contain any relations of length 3. Furthermore, we prove that, given two geodesic words representing the same element, one ca…
View article: Parabolic subgroups of Artin groups of FC type
Parabolic subgroups of Artin groups of FC type Open
Parabolic subgroups are the building blocks of Artin groups. This paper extends previous results, known only for parabolic subgroups of finite type Artin groups, to parabolic subgroups of FC type Artin groups. We show that the class of fin…
View article: Artin groups of infinite type: Trivial centers and acylindrical hyperbolicity
Artin groups of infinite type: Trivial centers and acylindrical hyperbolicity Open
While finite type Artin groups and right-angled Artin groups are well understood, little is known about more general Artin groups. In this paper we use the action of an infinite type Artin group on a CAT(0) cube complex to prove that has…
View article: Artin groups of infinite type: trivial centers and acylindical hyperbolicity
Artin groups of infinite type: trivial centers and acylindical hyperbolicity Open
While finite type Artin groups and right-angled Artin groups are well-understood, little is known about more general Artin groups. In this paper we use the action of an infinite type Artin group $A_Γ$ on a CAT(0) cube complex to prove that…
View article: Tilt: The Video - Designing Worlds to Control Robot Swarms with Only Global Signals
Tilt: The Video - Designing Worlds to Control Robot Swarms with Only Global Signals Open
We present fundamental progress on the computational universality of swarms of micro- or nano-scale robots in complex environments, controlled not by individual navigation, but by a uniform global, external force. More specifically, we con…