2003/04/15 by Zlil Sela
Mathematics · #math.GR #msc:14 #msc:20
published as Proceedings of the ICM, Beijing 2002, vol. 2, 87--92
arxiv created 2003/04/15 · arxiv updated 2009/11/30
We study sets of solutions to equations over a free group, projections of such sets, and the structure of elementary sets defined over a free group. The structre 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 (Gromov) hyperbolic groups will also be discussed.