An introduction to right-angled Artin groups

R Charney - Geometriae Dedicata, 2007 - Springer
Recently, right-angled Artin groups have attracted much attention in geometric group theory.
They have a rich structure of subgroups and nice algorithmic properties, and they give rise to …

[图书][B] Handbook of computational group theory

DF Holt, B Eick, EA O'Brien - 2005 - taylorfrancis.com
The origins of computation group theory (CGT) date back to the late 19th and early 20th
centuries. Since then, the field has flourished, particularly during the past 30 to 40 years, and …

Braid groups are linear

D Krammer - Annals of Mathematics, 2002 - JSTOR
In a previous work [11], the author considered a representation of the braid group ρ: Bn→
GLm (Z [q±1, t±1])(m= n (n-1)/2), and proved it to be faithful for n= 4. Bigelow [3] then proved …

Gaussian groups and Garside groups, two generalisations of Artin groups

P Dehornoy, L Paris - Proceedings of the London Mathematical …, 1999 - cambridge.org
It is known that a number of algebraic properties of the braid groups extend to arbitrary finite
Coxeter-type Artin groups. Here we show how to extend the results to more general groups …

The K (π, 1)-problem for hyperplane complements associated to infinite reflection groups

R Charney, MW Davis - Journal of the American Mathematical Society, 1995 - JSTOR
We begin by recalling some well-known facts. The natural action of the symmetric group Sn
on Rncan be viewed as a group generated by reflections. The reflections in Sn are the …

Groupes de garside

P Dehornoy - Annales scientifiques de l'Ecole normale supérieure, 2002 - Elsevier
Résumé Les monoı̈des de Garside sont introduits comme monoı̈des simplifiables où
existent ppcm et pgcd et où sont satisfaites des conditions convenables de finitude, et les …

Braids: a survey

JS Birman, TE Brendle - Handbook of knot theory, 2005 - Elsevier
Publisher Summary Crossings are suggested as they are in a picture of a highway overpass
on a map. The identity braid has a canonical representation in which two strands never …

The braid group B4 is linear

D Krammer - Inventiones mathematicae, 2000 - Springer
The braid group B4 is linear Page 1 Digital Object Identifier (DOI) 10.1007/s002220000088
Invent. math. 142, 451–486 (2000) The braid group B4 is linear Daan Krammer ⋆ …

Non-positively curved aspects of Artin groups of finite type

M Bestvina - Geometry & Topology, 1999 - msp.org
Artin groups of finite type are not as well understood as braid groups. This is due to the
additional geometric properties of braid groups coming from their close connection to …

Lattices, injective metrics and the K (π, 1) conjecture

T Haettel - Algebraic & Geometric Topology, 2024 - msp.org
Starting with a lattice with an action of ℤ or ℝ, we build a Helly graph or an injective metric
space. We deduce that the ℓ∞ orthoscheme complex of any bounded graded lattice is …