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Geometric and asymptotic group theory

Introduction to RAAGs

Lecture by Goulnara Arzhantseva
Problem session by Damian Osajda
Dienstag, 10:00-12:00, Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock

The purpose of this course is to give an elementary introduction to RAAGs. A right-angled Artin group (or briefly, a RAAG), also known as a partially commutative group (or a PC-group), associated to a graph is the group generated by the vertex set of the graph with commutation relators between adjacent vertices. That is, to specify a right-angled Artin group, it suffices to specify the graph.
Right-angled Artin groups arise naturally in several branches of mathematics and computer science. They have an extremely rich structure of subgroups which was explored in very recent proofs of 2 famous conjectures:

Baumslag's conjecture’68: Every 1-relator group with torsion is residually finite.

Virtual Haaken conjecture’(Waldhausen’68): Every aspherical closed 3-manifold has a finite cover which is Haken.

The course is open to students of all degrees (Bachelor, Master or PhD). The knowledge of the following fundamental concepts is required: graph, group, algebra, presentation of a group by generators and relators, fundamental group, covering space.

Course assessment: Presentation or test.

The first hour (10:00-10:45) is a lecture, and the second hour (11:00-11:45) is a problem session.

Lists of problems: Blatt 1, Blatt 2, Blatt 3, Blatt 4, Blatt 5, Blatt 6

List of exam questions: Exam