Results 1 to 10 of about 3,969 (116)
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. We also show that every right-angled Artin group can be embedded in a pure surface braid group. On the other hand, by generalising to right-angled
Crisp, John, Wiest, Bert
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Braid pictures for Artin groups [PDF]
Transactions of the American Mathematical Society, 2002 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, tilde{B}_n, tilde{C}_n and tilde{D}_n as subgroups of the braid groups of various simple orbifolds ...
Allcock, Daniel
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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
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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
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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.
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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
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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
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On braid groups and right-angled Artin groups [PDF]
Geometriae Dedicata, 2014 A \textit{right-angled Artin group} is a group with a presentation whose only relators are commutators between generators. A. Abrams and R. Ghrist conjectured in [\textit{A. Abrams}, Geom. Dedicata 92, 185--194 (2002; Zbl 1049.20023)] and [\textit{R. Ghrist}, AMS/IP Stud. Adv. Math.
Connolly, Francis, Doig, Margaret
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Topological model of composite fermions in the cyclotron band generator picture: New insights
Results in Physics, 2018 A combinatorial group theory in the braid groups is correlated with the unusual “anyon” statistic of particles in 2D Hall system in the fractional quantum regime well.
Beata Staśkiewicz
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A polynomial algorithm for the braid double shielded public key cryptosystems
Қарағанды университетінің хабаршысы. Математика сериясы, 2016 We propose new provable practical deterministic polynomial time algorithm of cryptographic analysis for the braid Wang, Xu, Li, Lin and Wang «Double shielded public key cryptosystems», where the authors recommended the Artin braid groups Bn as platforms
V.A. Roman’kov
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