Results 1 to 10 of about 85 (66)
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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On the linearity of Artin braid groups
Journal of Algebra, 2003 The author proves that all Artin groups of crystallographic type have a faithful representation of dimension the number of reflections of the associated Coxeter group. The faithfulness criterion which is used is that of \textit{D. Krammer} [Ann. Math. (2) 155, No. 1, 131-156 (2002; Zbl 1020.20025)].
François Digne
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Embeddings of graph braid and surface groups in right-angled Artin groups and braid groups [PDF]
Algebraic and 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
Bert Wiest, Wiest Bert
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Embedding right-angled Artin groups into graph braid groups [PDF]
Geometriae Dedicata, 2006 We construct an embedding of any right-angled Artin group $G(Δ)$ defined by a graph $Δ$ into a graph braid group. The number of strands required for the braid group is equal to the chromatic number of $Δ$. This construction yields an example of a hyperbolic surface subgroup embedded in a two strand planar graph braid group.
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Almost-crystallographic groups as quotients of Artin braid groups
Journal of Algebra, 2019 Let $n, k \geq 3$. In this paper, we analyse the quotient group $B\_n/Γ\_k(P\_n)$ of the Artin braid group $B\_n$ by the subgroup $Γ\_k(P\_n)$ belonging to the lower central series of the Artin pure braid group $P\_n$. We prove that it is an almost-crystallographic group. We then focus more specifically on the case $k=3$. If $n \geq 5$, and if $τ\in N$
OSCAR Ocampo +2 more
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A quotient of the Artin braid groups related to crystallographic groups
Journal of Algebra, 2017 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
OSCAR Ocampo +2 more
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Some subgroups of Artin's braid group
Topology and Its Applications, 1997 The braid group \(B_n\) has the presentation \[ \langle\sigma_1,\dots,\sigma_{n-1};\;\sigma_i=\sigma_j\;(|i-j|>1),\;\sigma_i\sigma_j\sigma_i=\sigma_j\sigma_i\sigma_j\;(|i-j|=1)\rangle. \] Let \(S_n\) denote the group of permutations of the set \(A_n=\{1,\dots,n\}\). There exists the standard homomorphism \(h\colon B_n\to S_n\), such that \(h(\sigma_i)=(
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Conjugacy Problem for Subgroups with Applications to Artin Groups and Braid Type Group
Communications in Algebra, 2006 Let $G$ be a group endowed with a solution to the conjugacy problem and with an algorithm which computes the centralizer in $G$ of any element of $G$. Let $H$ be a subgroup of $G$. We give some conditions on $H$, under which we provide a solution to the conjugacy problem in $H$. We apply our results to some Artin groups and braid type groups.
Nuno Franco
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An Artin relation of length n in the braid group
Discrete Mathematics, 1992 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Lower central series of Artin–Tits and surface braid groups
Journal of Algebra, 2008 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Paolo Bellingeri
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