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# Towers and elementary embeddings in total relatively hyperbolic groups (Christopher Perez, Loyola University New Orleans)

## May 2, 2023 @ 12:15 pm - 1:10 pm

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, and independently Olga Kharlampovich and Alexei Myasnikov did the same using equivalent structures they called regular NTQ groups. 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.