Beyond Serre's "Trees" in two directions: Λ--trees and products of trees

2017/10/27 by Kharlampovich, Olga, Vdovina, Alina
#20.02 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1710.10306

Abstract

Serre in "Trees" laid down the fundamentals of the theory of groups acting on simplicial trees. In particular, Bass-Serre theory makes it possible to extract information about the structure of a group from its action on a simplicial tree. Serre's original motivation was to understand the structure of certain algebraic groups whose Bruhat--Tits buildings are trees. In this survey we will discuss the following generalizations of ideas from "Trees": the theory of isometric group actions on Λ-trees and the theory of lattices in the product of trees where we describe in more detail results on arithmetic groups acting on a product of trees.

Related

• Completely Metrisable Groups Acting on Trees
• An introduction to the local-to-global behaviour of groups acting on trees and the theory of local action diagrams
• Groups acting faithfully on trees and properly on products of trees
• Groups acting on trees with Tits' independence property (P)
• Groupes profinis presqu'amalgamés