Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
On representations of Artin–Tits and surface braid groups
View through CrossRef
AbstractWe define and study extensions of the Artin and Perron–Vannier representations of braid groups to topological and algebraic generalizations of braid groups. We provide faithful representations of braid groups of oriented surfaces with boundary as automorphisms of finitely generated free groups. The induced representations of such groups as outer automorphisms of finitely generated free groups are still faithful. Also we give a representation of braid groups of closed surfaces as outer automorphisms of finitely generated free groups. Finally, we provide faithful representations of Artin–Tits groups of type ???? as automorphisms of free groups.
Title: On representations of Artin–Tits and surface braid groups
Description:
AbstractWe define and study extensions of the Artin and Perron–Vannier representations of braid groups to topological and algebraic generalizations of braid groups.
We provide faithful representations of braid groups of oriented surfaces with boundary as automorphisms of finitely generated free groups.
The induced representations of such groups as outer automorphisms of finitely generated free groups are still faithful.
Also we give a representation of braid groups of closed surfaces as outer automorphisms of finitely generated free groups.
Finally, we provide faithful representations of Artin–Tits groups of type ???? as automorphisms of free groups.
Related Results
Résultats sur les extensions singulières des groupes d'Artin et de tresses virtuelles
Résultats sur les extensions singulières des groupes d'Artin et de tresses virtuelles
Cette thèse se propose d’étudier deux objets liés aux monoïdes de tresses singulières, le morphisme de désingularisation et la famille des invariants de Vassiliev, transposés dans ...
Automorphisms of right-angled Artin groups
Automorphisms of right-angled Artin groups
Automorphismes des groupes d'Artin à angles droits
Cette thèse a pour objet l’étude des automorphismes des groupes d’Artin à angles droits. Etant donné un graphe si...
Extra-pair paternity variation in two passerine birds breeding in a gradient of urbanisation
Extra-pair paternity variation in two passerine birds breeding in a gradient of urbanisation
Urbanisation has been increasing worldwide in recent decades, driving environmental change and exerting novel selective pressures on wildlife. Phenotypic differences between urban ...
Right-Angled Artin Groups
Right-Angled Artin Groups
This chapter deals with right-angled Artin groups, a broad spectrum of groups that includes free groups on one end, free abelian groups on the other end, and many other interesting...
Topological and algebraic aspects of virtual Artin groups
Topological and algebraic aspects of virtual Artin groups
Aspects topologiques et algébriques des groupes d'Artin virtuels
Cette thèse est consacrée à l'étude des groupes d'Artin virtuels, une classe de groupes récemment i...
Emil Artin: Ein musischer Mathematiker
Emil Artin: Ein musischer Mathematiker
Ein Porträt des brillanten Wissenschaftlers Emil Artin als vielseitig interessierten und künstlerisch begabten Menschen sowie als Emigranten, der nach Deutschland zurückkehrte. Em...
Helly meets Garside and Artin
Helly meets Garside and Artin
AbstractA 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...
Advantages of social foraging of Willow Tits Parus montanus
Advantages of social foraging of Willow Tits Parus montanus
The mean number of Willow Tits Parus montanus in single‐species flocks was significantly larger than in mixed‐species flocks of Willow and Coal Tits P. ater. Both flock size and th...