scholarly journals Random outer automorphisms of free groups: Attracting trees and their singularity structures

2021 ◽  
pp. 1
Author(s):  
Ilya Kapovich ◽  
Joseph Maher ◽  
Catherine Pfaff ◽  
Samuel J. Taylor
Keyword(s):  
Free Groups ◽  
Automorphisms Of Free Groups ◽  
Outer Automorphisms

On representations of Artin–Tits and surface braid groups

2011 ◽  
Vol 14 (1) ◽  
Author(s):  
Valeriy G. Bardakov ◽  
Paolo Bellingeri
Keyword(s):  
Free Groups ◽  
Braid Groups ◽  
Finitely Generated ◽  
Induced Representations ◽  
Automorphisms Of Free Groups ◽  
Closed Surfaces ◽  
Outer Automorphisms

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 𝒟 as automorphisms of free groups.

scholarly journals Normal automorphisms of free groups

1980 ◽  
Vol 64 (1) ◽  
pp. 52-53 ◽  
Author(s):  
Abraham S.-T. Lue
Keyword(s):  
Free Groups ◽  
Automorphisms Of Free Groups
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