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Israel Journal of Mathematics

, Volume 147, Issue 1, pp 1–73 | Cite as

Diophantine geometry over groups III: Rigid and solid solutions

Article

Abstract

This paper is the third in a series on the structure of sets of solutions to systems of equations in a free group, projections of such sets, and the structure of elementary sets defined over a free group. In the third paper we analyze exceptional families of solutions to a parametric system of equations. The structure of the exceptional solutions, and the global bound on the number of families of exceptional solutions we obtain, play an essential role in our approach towards quantifier elimination in the elementary theory of a free group presented in the next papers of this series. The argument used for proving the global bound is a key in proving the termination of the quantifier elimination procedure presented in the sixth paper of the series.

Keywords

Cayley Graph Limit Group Vertex Group Edge Group Abelian Decomposition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© The Hebrew University Magnes Press 2005

Authors and Affiliations

  • Z. Sela
    • 1
  1. 1.Institute of MathematicsThe Hebrew University of JerusalemJerusalemIsrael

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