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Preprint Number 1833

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1833. Christopher Perez
Towers and elementary embeddings in toral relatively hyperbolic groups

Submission date: 25 August 2020


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 result to toral relatively hyperbolic groups using JSJ and shortening techniques.

Mathematics Subject Classification: 20F67

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Full text arXiv 2008.10964: pdf, ps.

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