19217011

SoSe 15: Seminar zur Topologie

Holger Reich; Elmar Vogt

Hinweise für Studierende

Eine Vorbesprechung findet
am Mittwoch, 8.04., um 11:00 Uhr
in SR 031, Arnimallee 7, statt.
Anmeldung über das KVV. Schließen

Kommentar

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.

Literature:
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).

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. Schließen