CAT(0) Cube Complexes and Low Dimensional Cohomology, lecture 2
Presenter
August 18, 2016
Keywords:
- geometric group theory
- CAT(0) space
- cube complex
- quasi-isomorphisms
- rigidity results
- lattices in Lie groups
- solvable groups
- discrete group actions
- cohomology theory
- manifolds with boundary
- amenable groups
- Lipschitz continuity
MSC:
- 20F65
- 20F67
- 20Fxx
- 20-xx
- 37A20
- 22E40
- 43A07
- 52C25
Abstract
CAT(0) cube complexes are charming objects with many striking properties. For example, they admit two interesting, and naturally coupled metrics: the CAT(0) metric and the median metric, allowing one to access the rich tools from each of those worlds. The study of low dimensional cohomology of a group touches upon several important aspects of group theory: Property (T), the Haagerup Property, stable commutator length, and even superrigidity. In this talk, we will discuss CAT(0) cube complexes, and how they provide a nice framework for finding low dimensional cohomology classes such as the Haagerup Cocycle and various generalization of the Brooks cocycle.