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Talk

Geometric obstructions to measured Property (T)

  • Hector Jardon Sanchez (Leipzig University)
E2 10 (Leon-Lichtenstein)

Abstract

Measured Property (T) is a generalization of group Property (T) to graphings. An example of a graphing is obtained from a measure-preserving action of a group on a standard probability space by drawing the Cayley graph of said group in each orbit. Further examples of graphings include, for instance, and very roughly speaking, regraphings of this previous graph by local or random algorithms.

This talk is an invitation to the following question: what geometries can appear in graphings with measured Property (T)? For instance, one cannot obtain graphings whose components are acyclic or planar. This will be discussed in the talk, together with all the necessary background. In the group case, it follows from Thurston's Geometrization Conjecture that an infinite Property (T) group cannot appear as the fundamental group of a compact 3-manifold. How does this fact translate to the measured setting, and what further geometric obstructions to measured Property (T) can occur?

This talk is based on joint work with Łukasz Grabowski and Sam Mellick, as well as on an on-going project with Antoine Poulin.

Upcoming Events of this Seminar