Simon Thomas
An Introduction to Geometric Group Theory
This course will be an introduction to Geometric Group Theory. There are no prerequisites, except for the most basic notions of group theory. In Geometric Group Theory, finitely generated groups are viewed as metric spaces via the path metrics on their Cayley graphs and their large-scale geometry is studied. The topics covered in this course will include:
(i) Quasi-isometries and the large-scale geometry of finitely generated groups.
(ii) Growth rates of finitely generated groups, including the construction of groups of intermediate growth.
(iii) The basic theory of amenable groups.
Pierre de la Harpe, Topics in Geometric Group Theory, Chicago, 2000.
Basic group theory