Autumn Semester 2020 takes place in a mixed form of online and classroom teaching. Please read the published information on the individual courses carefully.
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.
Objective
Introduction to the general theory of group actions on trees, also known as Bass-Serre theory, and various important results on decompositions of groups.
Content
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.
Literature
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
Prerequisites / Notice
Familiarity with the basics of fundamental group (and covering theory).
Performance assessment
Performance assessment information (valid until the course unit is held again)
Performance assessment as a semester course