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

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

2003-04-15

arxiv.org/abs/math/0304209v1

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

Mathematics

Group Theory

Scientific paper

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.

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