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Cohomological Induction and uniform measure equivalence

Cohomological Induction and uniform measure equivalence
Date:

07.11.2019

Place:

2.058 (20.30)

Speaker:

Thomas Gotfredsen

Time:

15:45

Abstract: In the beginning of the century it has been shown by Shalom and Sauer that for discrete groups, group cohomology interacts well with the notion of quasi-isometry, and, for amenable groups, coincides with the notion of uniform measure equivalence. Bader, Furman and Sauer have since then defined a notion for measure equivalence in the locally compact case, and it has been proven by Koivisto, Kyed and Raum that their notion of uniform measure equivalence coincides with quasi-isometry if the groups in question are amenable.
In my talk, I will present an induction isomorphism arising from a uniform measure equivalence of locally compact second countable unimodular groups, generalising the result of Sauer, showing that their real cohomology rings coincide. I will further show, how this can be applied to provide new insights into the quasi-isometry classification problem for low dimensional nilpotent Lie groups. This is joint work with David Kyed.