250012 VO Selected topics in graph theory - "Graphs and Groups"

* Monday 13:05-14:05 in 2A310 (UZA2), second floor (the usual lecture room)
* Tuesday 13:05-15:05 (with 10 Min. break) in 2A180 (UZA2), ground floor
* Wednesday 9:05-10:05 in 2A310 (UZA2), second floor
* Additional lecturs on Friday December 12, 2008, 9:30-12:00 and 13:00-15:00, C2.09 UZA2 (with breaks).


If requested by students, the lecture will be held in English, otherwise in German.

2008/09 Lecture "Graphs and Groups - Ends of Graphs and Groups"
German: VL Ausgewählte Kapitel der Graphentheorie (Graphen und Gruppen - Enden von Graphen und Gruppen)


There will be no problem class (Übungen) to this lecture. But we will discuss many examples during the lecture. You can earn bonus points for the final examination by preparing these examples at home.

Topics of the lecture: automorphisms of graphs, Cayley-graphs, ends of graphs, end-compactifications, Dunwoody's structure-tree theory, Stallings' Structure Theorem etc.

Most of the time we will study the part of infinite graph theory which deals with group actions. (For those who have been in my lecture on combinatorics: note that this has not much to do with Pólya theory. In the present lecture we are not enumerating, but studying geometric structures.) The topics are related to the field of geometric group theory, an important and popular branch of modern Mathematics. One goal of the lecture is to devolpe an old handout on "Ends of graphs" further to a monograph.

You do not have to be well grounded in graph theory in order to follow the lecture. But it would be an advantage if you have heard about elementary concepts of topology (compactness, convergence, accumulation points,...) and group theory (index of a subgroup, normal subgroups, cosets, generating sets,...). If necessary, I will of course repeat definitions and basic results. Contact me if you are not sure wether this lecture is suitable for you or not.

This course is highly recommended for students who want to write a diploma or PhD thesis under my supervision.


Preliminary contents:

Enden von Graphen und Gruppen

Teil 1: Enden von Graphen
Teil 2: Automorphismen und Enden Teil 3: Strukturbäume Teil 4: Enden von Gruppen

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