442504 VO Geometric and asymptotic group theory (2013W)

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’67: 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.