Elementary embeddings in torsion-free hyperbolic groups

Abstract

We consider embeddings in a torsion-free hyperbolic group which are elementary in the sense of first-order logic. We give a description of these embeddings in terms of Sela's hyperbolic towers. We deduce as a corollary that subgroups elementarily embedded in finitely generated free groups are free factors.

arXiv commentThe statement and the proof of Proposition 5.11 are corrected. All the other results remain unchanged