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arXiv · 1710.10306

Beyond Serre's "Trees" in two directions: $\Lambda$--trees and products of trees

Olga Kharlampovich·Alina Vdovina
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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 $\Lambda$-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.

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Olga Kharlampovich, Alina Vdovina. 2017-10-27. Beyond Serre's "Trees" in two directions: $\Lambda$--trees and products of trees. https://arxiv.org/abs/1710.10306

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