Ruprecht-Karls-Universität Heidelberg

Seminar: Groups acting on trees

Sommersemester 2018

JProf. Dr. Maria Beatrice Pozzetti



Schedule

  • Tuesday 16:00-18:00 INF 205, Room SR 3

Msli

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

Description

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 Matemtica Complutense vol. 16(2003), no. 1, pp. 5-101
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