Diophantine geometry over groups and the elementary theory of a free group.
by
Zlil Sela
Hebrew University and IAS

We study the structure of sets of solutions to equations defined over a free group, projections of such sets, and the structure of elementary sets defined over a free group. The structure theory we obtain, enable us to answer some questions of A. Tarski's, and classify those finitely generated groups that are elementary equivalent to a free group. Connections with low dimensional topology, and a generalization to general hyperbolic groups and their elementary classification, will also be discuseed.

Date received: February 21, 2002