** Geometric and asymptotic group theory **

Gromov's polynomial growth theorem

Lecture by Goulnara Arzhantseva

and

Problem session by Damian Osajda

Dienstag, 10:00--12:00, Raum 2A310 UZA2

This course is aimed to present basic notions and techniques used within Geometric Group Theory. In particular we focus on the growth function. The ultimate goal is to demonstrate Kleiner's proof of Gromov's polynomial growth theorem.

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__, __Blatt 7__, __Blatt 8__,
__Blatt 9__, __Blatt 10__

- Quasi-isometries:

Ch. 1.8. of the book by Bridson, Martin R., Haefliger, Andre, Metric spaces of non-positive curvature

- Free groups and group presentations:

Ch. 2 (pages 45 -69) of the book by Bogopolski, Oleg, Introduction to group theory

- Growth of groups:

Ch. 1, Ch. 3.1 and 3.2 of Nick, Scott, Growth of Finitely Generated Groups, available

- Subgroups distortion (advanced reading):

Mitra, Mahan, Coarse extrinsic geometry: a survey, available

Ch 3. of the book Gromov, Michael, Asymptotic invariants of infinite groups.