Abstract: We study an important class of discrete groups in detail following [Gu ́e+17, Chapter 2.1]. First we
consider the definition of a hyperbolic group Γ (also called Gromov hyperbolic or word hyperbolic),
focusing on the group itself rather than its Cayley graph, and not wasting time on the general theory
of hyperbolic metric spaces. Then we study the notion of the boundary ∂Γ, its topology, and the most
important properties of the Γ-action on ∂Γ (this is a main goal of the talk). Furthermore, we study the
following topics:
Classification of elements of Γ according to their action on ∂Γ
The Γ-equivariant homeomorphism ∂Γ ∼= Λ(Γ). In the case Γ ⊂Iso(Hn+1), see [Bow93]
Examples and non-examples of hyperbolic groups. Illustration of the above concepts in some
examples
If time allows:
Detailed study of the example of the fundamental group of a closed Riemannian manifold of negative
curvature
The Gromov flow space
Date
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Thursday, 23.11.2023
| 09.15 to 10.45 h
Study Group "Patterson-Sullivan Theory": Benjamin Hinrichs, "Hyperbolic groups"
Location: D2.314