In Geometric Group Theory, we study groups by their action on "nice" metrics spaces. The purpose of this lecture is to overview this vast developing theory. The fundamental idea of Geometric Group Theory comes from its relation to geometric structures on manifolds. In particular, it has a fruitful relationship with hyperbolic geometry. Therefore I will also spend a reasonable time on hyperbolic geometry.
To understand basic properties Geometric Group Theory.
To be familiar with the basics of geometric structures on manifolds.
Geometric Group Theory, Hyperbolic Groups, Geometric Structures, Hyperbolic Geometry
|✔ Specialist skills||Intercultural skills||Communication skills||Critical thinking skills||Practical and/or problem-solving skills|
standard lecture course
|Course schedule||Required learning|
|Class 1||Fundamental Groups and Universal Coverings||Details will be provided during each class session|
|Class 2||Geometric Structures on Manifolds|
|Class 3||Presentations of Groups|
|Class 4||Group Actions|
|Class 5||Quasi-isometric Mappings|
|Class 6||Hyperbolic Geometry|
|Class 7||Teichmuler Space|
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
Clara Loeh, Geometric Group Theory: An Introduction (Universitext)
Basic knowledge of groups and manifolds would help to understand this lecture.
The lecture plan might be changed