C. Perin: Subgroups elementarily embedded in torsion-free hyperbolic groups.

Abstract: A subgroup H of a group G is said to be elementarily embedded if G and H satisfy the same first order formulas in which we allow the use of elements of H as constants.

The aim of this talk is to give a description of this embedding in the case where G is torsion-free hyperbolic. We will see that in this case, G can be given a structure of hyperbolic tower over H. This is of course reminiscent of Sela's description of elementarily free groups, and in fact the proofs are very similar. It is interesting to note that in the special case of free group, the result implies that the only elementarily embedded subgroups must be free factors.