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# Claremont Topology Seminar: Christopher Perez (Loyola University New Orleans)

## October 10, 2023 @ 3:00 pm - 4:00 pm

Title: Towers and elementary embeddings in total relatively hyperbolic groups

Abstract: 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 ChloĆ© 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.