arXiv:math/0304209 Abstract

arXiv:math/0304209 [math.GR]Abstract References Reviews Resources

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

Published 2003-04-15Version 1

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.

Journal: Proceedings of the ICM, Beijing 2002, vol. 2, 87--92

Categories: math.GR

Keywords: hyperbolic groups, diophantine geometry, elementary theory, free group, low dimensional topology

Tags: journal article

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