University of Illinois Chicago
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Measurable Imbeddings: An Order-like Generalization of Measure Equivalence

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posted on 2024-08-01, 00:00 authored by Ahmet Özkan Demir
We introduce and explore the notion of Measurable Imbedding, which gives a partial ordering among discrete countable groups. We show it behaves nicely under some group-theoretic operations like free products and graph products (generalizing the same results for Orbit Equivalence). Then, we explore rigidity and flexibility for this notion and prove some rigidity results for lattices in higher rank simple Lie groups (generalizing the same results for Measure Equivalence rigidity). Finally, we introduce a new invariant called measurable free rank, which can be thought of as a measurable version of noncommutative free subgroup rank of a group (introduced by Campagnolo and Kammeyer) and compute it for non-elementary hyperbolic groups as 1.

History

Advisor

Alex Furman

Department

Mathematics, Statistics, and Computer Science

Degree Grantor

University of Illinois Chicago

Degree Level

  • Doctoral

Degree name

Doctor of Philosophy

Committee Member

Daniel Groves Osama Khalil Wouter van Limbeek Tsachik Gelander

Thesis type

application/pdf

Language

  • en

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