Seminar: Groups acting on trees

Sommersemester 2018

JProf. Dr. Maria Beatrice Pozzetti

Müsli

Please, register for the seminar on MÜSLI, and send me an e-mail (pozzetti@mathi.uni-heidelberg.de).

The seminar will focus on properties of groups acting on tree and Bass-Serre theory. 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.

We will cover the following topics.

Amalgams and HNN extensions.
Free groups and their subgroups.
The general theory of actions on trees, i.e, Bass-Serre theory.
Stallings' theorem.

At the organizational meeting several topics will be proposed. Among them, you can choose one topic you are interested in. Once you have agreed on the topic of your project with us, you should contact me to discuss the content of your talk in more detail. Please let me help you during the preparation of your presentation. You are expected to hand in a short report one week before your presentation.

Here is a syllabus of the talks.

Prerequisites

This seminar is aimed at students who are interested in geometry and group theory. Familiarity with the basics of fundamental group and covering theory are expected. There are several topics for students to choose from, and hence any interested student is welcome to attend. The seminar is open for bachelor and master students, and will be taught in English.

Schedule of the talks


17.04.2017	organization meeting
24.04.2017	Beatrice Pozzetti	Talk 1: Amalgams
08.05.2017	Patrick Scholz	Talk 2: Trees
15.05.2017	Mareike Pfeil	Talk 3: Free Groups
22.05.2017	Caroline Edmaier	Talk 4:Trees and amalgams
29.05.2017	Paul Gontschar	Talk 5: Trees of groups
05.06.2017	Beatrice Pozzetti	Talk 6: Fundamental groups
12.06.2017	Beatrice Pozzetti	Talk 7: Universal coverings
19.06.2017	Ferdinand Vanmaele	Talk 8: Property (FA)
26.06.2017	Ferdinand Vanmaele	Talk 9: Coxeter groups with (FA)

References

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