Results 11 to 20 of about 51,088 (236)
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
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Subgroup separability of Artin groups [PDF]
Journal of Algebra, 2021 15 pages, to be published in Journal of ...
Kisnney Almeida, Igor Lima
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Right‐angled Artin subgroups of Artin groups
Journal of the London Mathematical Society, 2022 The Tits Conjecture, proved by Crisp and Paris, states that squares of the standard generators of any Artin group generate an obvious right-angled Artin subgroup. We consider a larger set of elements consisting of all the centers of the irreducible spherical special subgroups of the Artin group, and conjecture that sufficiently large powers of those ...
Jankiewicz, Kasia, Schreve, Kevin
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Cohomology of Artin Groups [PDF]
Mathematical Research Letters, 1996 Let \(W,S\) be a Coxeter system realized as an irreducible reflection group in \(\mathbb{R}^n\). Denote by \(A=(H)\) the arrangement of reflection hyperplanes and by \(G_W\) the corresponding Artin group. The authors introduce some combinatorial complex \(X_W\) which is homotopically equivalent to the orbit space \((\mathbb{C}^n -\bigcup_{H \in A ...
De Concini, C., Salvetti, M.
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Proceedings of the London Mathematical Society, 2022 Starting from the observation that the standard presentation of a virtual braid group mixes the standard presentation of the corresponding braid group with the standard presentation of the corresponding symmetric group and some mixed relations that mimic the action of the symmetric group on its root system, we define a virtual Artin group $VA[ ]$ of a
Bellingeri, Paolo +2 more
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Relative Hyperbolicity and Artin Groups [PDF]
Geometriae Dedicata, 2004 Let $G=$ be an Artin group and let $m_{ij}=m_{ji}$ be the length of each of the sides of the defining relation involving $a_i$ and $a_j$. We show if all $m_{ij}\ge 7$ then $G$ is relatively hyperbolic in the sense of Farb with respect to the collection of its two-generator subgroups $$ for which $m_{ij}
Kapovich, Ilya, Schupp, Paul
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Ibn Al-Haitham Journal for Pure and Applied Sciences, 2023 The set of all (n×n) non-singular matrices over the field F. And this set forms a group under the operation of matrix multiplication. This group is called the general linear group of dimension over the field F, denoted by .
Niran sabah Jasim +2 more
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Bicyclic commutator quotients with one non-elementary component [PDF]
Mathematica Bohemica, 2023 For any number field $K$ with non-elementary $3$-class group ${\rm Cl}_3(K)\simeq C_{3^e}\times C_3$, $e\ge2$, the punctured capitulation type $\varkappa(K)$ of $K$ in its unramified cyclic cubic extensions $L_i$, $1\le i\le4$, is an orbit under the ...
Daniel C. Mayer
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k-Parabolic Subspace Arrangements [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 In this paper, we study k-parabolic arrangements, a generalization of the k-equal arrangement for any finite real reflection group. When k=2, these arrangements correspond to the well-studied Coxeter arrangements.
Christopher Severs, Jacob White
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Artin groups of Euclidean type [PDF]
Inventiones mathematicae, 2017 This article resolves several long-standing conjectures about Artin groups of euclidean type. In particular, we prove that every irreducible euclidean Artin group is a torsion-free centerless group with a decidable word problem and a finite-dimensional classifying space.
McCammond, Jon, Sulway, Robert
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