This course will introduce the audience to different aspects of geometry group theory. The starting point is the introduction of the Calyley graph of a finitely generated group and geometric notion of quasi-isometry. Subsequently, four different topics are discussed:
• Growth in groups and Gromov’s theorem on virtually nilpotent groups
• Hyperbolic groups and the Gromov boundary
• Ends and Stalling’s theorem
• Amenability
• De la Harpe - "Topics in Geometric Group Theory"
• Druţu Kapovich - “Geometric Group Theory”
• Graph theory, and
• Metric spaces.
• Growth in groups and Gromov’s theorem on virtually nilpotent groups
• Hyperbolic groups and the Gromov boundary
• Ends and Stalling’s theorem
• Amenability
The subject of geometric group theory displays lively interaction with many other areas of mathematics, such as algebraic topology, combinatorial group theory, Lie groups and operator algebras.
Literature: The main resource for the course will be Löh’s book “Geometric Group Theory – An Introduction”. The following additional references can be usefull
• Bridson Haeflinger - “Metric spaces of non-positive curvature”• De la Harpe - "Topics in Geometric Group Theory"
• Druţu Kapovich - “Geometric Group Theory”
Prerequisites: The course assumes only basic knowledge in
• Group theory,• Graph theory, and
• Metric spaces.
- Kursleiter:in: Dr. Sanaz Pooya
- Kursleiter:in: Prof. Dr. Sven Raum