Autumn Semester 2020 takes place in a mixed form of online and classroom teaching.
Please read the published information on the individual courses carefully.

Nir Lazarovich: Catalogue data in Spring Semester 2017

Name Dr. Nir Lazarovich
Pool Gruppe 1 (D-MATH)
ETH Zürich, HG G 28
Rämistrasse 101
8092 Zürich

401-4206-17LGroup Actions on Trees4 credits2VN. Lazarovich
AbstractAs 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.
ObjectiveIntroduction to the general theory of group actions on trees, also known as Bass-Serre theory, and various important results on decompositions of groups.
ContentDepending 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.
LiteratureJ.-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 / NoticeFamiliarity with the basics of fundamental group (and covering theory).