English

Diophantine geometry over groups and the elementary theory of free and hyperbolic groups

Group Theory 2007-05-23 v1

Abstract

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.

Keywords

Cite

@article{arxiv.math/0304209,
  title  = {Diophantine geometry over groups and the elementary theory of free and hyperbolic groups},
  author = {Zlil Sela},
  journal= {arXiv preprint arXiv:math/0304209},
  year   = {2007}
}