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Towers and Elementary Embeddings in Toral Relatively Hyperbolic Groups

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posted on 01.08.2020, 00:00 by Christopher Adam Perez
In a remarkable series of papers, Zlil Sela classified the first-order theories of free groups and torsion-free hyperbolic groups using geometric structures he called towers. It was later proved by Chloé Perin that if H is an elementarily embedded subgroup (or elementary submodel) of a torsion-free hyperbolic group G, then G is a tower over H. We prove a generalization of Perin's results to toral relatively hyperbolic groups using JSJ and shortening techniques.

History

Advisor

Groves, Daniel

Chair

Groves, Daniel

Department

Mathematic, Statistics, and Computer Science

Degree Grantor

University of Illinois at Chicago

Degree Level

Doctoral

Degree name

PhD, Doctor of Philosophy

Committee Member

Whyte, Kevin Van Limbeek, Wouter Einstein, Eduard Sela, Zlil

Submitted date

August 2020

Thesis type

application/pdf

Language

en

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