2024/2025

Gromov Hyperbolic Groups

Type: Optional course (faculty)

Delivered by: Faculty of Mathematics

Where: Faculty of Mathematics

When: 1, 2 module

Open to: students of all HSE University campuses

Instructors: Alexey Golota

Language: English

ECTS credits: 6

Contact hours: 60

Course Syllabus

Abstract

Historically, the study of infinite groups was primarily motivated by problems from geometry. On the other hand, geometric methods are widely used to explore the structure of groups. For instance, for a group with a finite set of generators one can define its Cayley graph and a natural left-invariant metric on it. In 1980s M. Gromov laid the foundations of a theory of <<hyperbolic>> groups, that is, the groups with Cayley graphs of <<negative curvature>> (in an appropriate sense). The class of hyperbolic groups is quite large, for example, it includes lattices in Lie groups of rank 1, fundamental groups of negatively-curved manifolds, free groups etc. The theory of hyperbolic groups is a rich theory with numerous applications. The goal of the course is to provide an introduction to this theory and, more generally, to study methods of geometric group theory via examples.