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CAT(0) Cube Complexes and Low Dimensional Cohomology

Connections for Women: Geometric Group Theory August 17, 2016 - August 19, 2016

August 18, 2016 (11:20 AM PDT - 12:10 PM PDT)
Speaker(s): Talia Fernos (University of North Carolina)
Location: MSRI:
  • 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

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC



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.

31104?type=thumb Notes 229 KB application/pdf Download
Video/Audio Files


H.264 Video 14580.mp4 348 MB video/mp4 rtsp://videos.msri.org/data/000/026/407/original/14580.mp4 Download
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