CAT(0) Cube Complexes and Low Dimensional Cohomology
Connections for Women: Geometric Group Theory August 17, 2016  August 19, 2016
Location: SLMath:
geometric group theory
CAT(0) space
cube complex
rigidity results
lattices in Lie groups
solvable groups
discrete group actions
cohomology theory
manifolds with boundary
amenable groups
Lipschitz continuity
20Jxx  Connections of group theory with homological algebra and category theory
00A35  Methodology of mathematics {For mathematics education, see 97XX}
14580
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.
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