Seminar zur Topologie
Zeit und Ort: Dienstag 16:00-18:00 Uhr, Arnimallee 7, SR E.31
Leistungsnachweis: Vortrag und schriftliche Vortragsausarbeitung.
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)
|Vorbesprechung / preliminary discussion
|Basic Notions and van Kampen theorem
|Free products with amalgamation and HNN extensions
| Elmar Vogt
|Seminar on Farrell-Jones-Conjecture
|Gruško's Theorem and the Kurosh subgroup theorem
| Arne Roland
|Subgroups and covering spaces
|Uniqueness of free product decompositions
|Graphs of groups I
|Graphs of groups II
|Graphs of groups III
|Ends of groups I
|Ends of groups II
- 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).