Course Overview: Group actions on \(\mathbb{R}\)-trees appear in many places in low-dimensional topology and geometric group theory. The aim of the course is to introduce some common tools for working with such actions and some key theorems in the area. The plan for the core of the course is:
- Classification of isometries
- Length functions and the Culler-Morgan theorem
- Foliated complexes and free actions of surface groups on trees
- Decomposing actions into mixing and indecomposable pieces
- Rips' theorem for free actions on R-trees
The remainder of the course will depend on time and audience interest but
can include topics such as:
- The Bestvina-Paulin construction for groups acting on hyperbolic spaces
- Spaces of trees; length function and Gromov-Hausdor topologies
- Laminations and the observer's topology
- Applications to automorphisms of free groups
Lecturer(s):
Dr Richard Wade