As a main theme, we will explain how an action of a group on a tree enables us to break the group into smaller pieces, and thus gain better understanding of its structure. After introducing the general theory, we will cover various topics in this general theme.
Introduction to the general theory of group actions on trees, also known as Bass-Serre theory, and various important results on decompositions of groups.
Depending on time we will cover some of the following topics. - Free groups and their subgroups. - The general theory of actions on trees, i.e, Bass-Serre theory. - Trees as 1-dimensional buildings. - Stallings' theorem. - Grushko's and Dunwoody's accessibility results. - Actions on R-trees and the Rips machine.
J.-P. Serre, Trees. (Translated from the French by John Stillwell). Springer-Verlag, 1980. ISBN 3-540-10103-9
C. T. C. Wall. The geometry of abstract groups and their splittings. Revista Matemática Complutense vol. 16(2003), no. 1, pp. 5-101
Voraussetzungen / Besonderes
Familiarity with the basics of fundamental group (and covering theory).
Information zur Leistungskontrolle (gültig bis die Lerneinheit neu gelesen wird)