Results 1 to 10 of about 3,993 (104)
Embeddings of graph braid and surface groups in right-angled Artin groups and braid groups [PDF]
Algebraic & Geometric Topology, 2004 We prove by explicit construction that graph braid groups and most surface groups can be embedded in a natural way in right-angled Artin groups, and we point out some consequences of these embedding results.
Bert Wiest +9 more
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Braid pictures for Artin groups [PDF]
Transactions of the American Mathematical Society, 1998 We define the braid groups of a two-dimensional orbifold and introduce conventions for drawing braid pictures. We use these to realize the Artin groups associated to the spherical Coxeter diagrams A_n, B_n=C_n and D_n and the affine diagrams tilde{A}_n ...
Allcock, Daniel
core +4 more sources
Embedding right-angled Artin groups into graph braid groups [PDF]
Geometriae Dedicata, 2010 We construct an embedding of any right-angled Artin group $G(\Delta)$ defined by a graph $\Delta$ into a graph braid group. The number of strands required for the braid group is equal to the chromatic number of $\Delta$.
A. Abrams +10 more
core +2 more sources
The $$R_\infty $$ property for pure Artin braid groups [PDF]
Monatshefte für Mathematik, 2021 In this paper we prove that all pure Artin braid groups $P_n$ ($n\geq 3$) have the $R_\infty$ property. In order to obtain this result, we analyse the naturally induced morphism $\operatorname{\text{Aut}}(P_n) \to \operatorname{\text{Aut}}(Γ_2 (P_n)/Γ_3(P_n))$ which turns out to factor through a representation $ρ\colon S_{n+1} \to \operatorname{\text ...
Karel Dekimpe +2 more
exaly +6 more sources
Higher Braid Groups and Regular Semigroups from Polyadic-Binary Correspondence
Mathematics, 2021 In this note, we first consider a ternary matrix group related to the von Neumann regular semigroups and to the Artin braid group (in an algebraic way).
Steven Duplij
doaj +1 more source
A GATHERING PROCESS IN ARTIN BRAID GROUPS [PDF]
International Journal of Algebra and Computation, 2006 In this paper we construct a gathering process by the means of which we obtain new normal forms in braid groups. The new normal forms generalize Artin–Markoff normal forms and possess an extremely natural geometric description. In the two last sections of the paper we discuss the implementation of the introduced gathering process and the questions ...
Esyp, Evgeinj S., Kazachkov, Ilya V.
openaire +4 more sources
Curve graphs for Artin–Tits groups of type B, A∼ and C∼ are hyperbolic
Transactions of the London Mathematical Society, 2021 The graph of irreducible parabolic subgroups is a combinatorial object associated to an Artin–Tits group A defined so as to coincide with the curve graph of the (n+1)‐times punctured disk when A is Artin's braid group on (n+1) strands.
Matthieu Calvez +1 more
doaj +1 more source
Helly meets Garside and Artin [PDF]
, 2021 A graph is Helly if every family of pairwise intersecting combinatorial balls has a nonempty intersection. We show that weak Garside groups of finite type and FC-type Artin groups are Helly, that is, they act geometrically on Helly graphs. In particular,
Huang, Jingyin, Osajda, Damian
core +3 more sources
Graph braid groups and right-angled Artin groups [PDF]
Transactions of the American Mathematical Society, 2011 We give a necessary and sufficient condition for a graph to have a right-angled Artin group as its braid group for braid index ≥ 5 \ge 5 . In order to have the necessity part, graphs are organized into small classes so that one of the homological or cohomological characteristics of right-angled Artin groups can be ...
Kim, JH Kim, Jee-Hyoun +2 more
openaire +3 more sources
On the structure of the centralizer of a braid [PDF]
, 2003 The mixed braid groups are the subgroups of Artin braid groups whose elements preserve a given partition of the base points. We prove that the centralizer of any braid can be expressed in terms of semidirect and direct products of mixed braid groups ...
Gonzalez-Meneses, Juan, Wiest, Bert
core +5 more sources