Sommersemester 2015

Dozenten:  Prof. Dr. Holger Reich,  Prof. Dr. Elmar Vogt

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• Zeit und Ort:  Dienstag  16:00-18:00 Uhr,  Arnimallee 7,  SR E.31

• Leistungsnachweis:  Vortrag und schriftliche Vortragsausarbeitung.

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Content:  Quite a few theorems in group theory have found fairly simple proofs using methods from topology. The connection between groups and topology is the fact that every group is the fundamental group of a topological space. For a given group there are many choices of topological spaces with this property, and choosing an appropriate space allows the use of tools from topology to attack the problem at hand. For example, once one knows that the fundamental group of a connected graph is a free group the theorem that subgroups of free groups are free becomes a simple application of covering space theory. 
Using topological and geometric methods in group theory has become a very active branch of mathematics. Our seminar introduces topological methods that have been used to prove results that give powerful insights into the structure of infinite groups. 
For the topologically minded we like to add that these group theoretic results are in return very helpful in topology. 

Target group:  The seminar is intended for students who have taken the Topology 1 course and thus have some familiarity with the fundamental group and covering spaces. In the first week of the semester we will summarize what will be needed later on. Also some basic facts and definitions from homology theory will be used in the later part of the seminar. These are covered in the Topology 2 course.

We encourage all participants to give their presentation in English, but anyone who absolutely panics at the thought of giving her/his talk in English might use German. (No other language, please)

Vorträge

Termin	Titel	Vortragende(r)
14.04.	Vorbesprechung / preliminary discussion
28.04.	Basic Notions and van Kampen theorem	Elmar Vogt
05.05.	Free products with amalgamation and HNN extensions	Elmar Vogt
12.05.	Seminar on Farrell-Jones-Conjecture	SFB 647
19.05.	Gruško's Theorem and the Kurosh subgroup theorem	Arne Roland
26.05.	Subgroups and covering spaces	Arne Roland
02.06.	Uniqueness of free product decompositions	Markus Penner
09.06.	Graphs of groups I	Vincent Boelens
16.06.	Graphs of groups II	Vincent Boelens
23.06.	Graphs of groups III	Reiner Backhaus
30.06.	Ends of groups I	Max Krause
07.07.	Ends of groups II	Max Krause

Literatur 

• The talks of the seminar are based on notes by Peter Scott and Terry Wall: Topological methods in group theory,
  London Mathematical Society Lecture Notes Series 36 (1979).