Date of Degree

9-2015

Document Type

Dissertation

Degree Name

Ph.D.

Program

Mathematics

Advisor

Olga Kharlampovich

Subject Categories

Mathematics

Keywords

elementary theory of groups; equations; generalized doubles; group theory; hyperbolic groups; limit groups

Abstract

We show that the Diophantine problem, for quadratic equations over a non-elementary torsion-free hyperbolic group, is NP-complete. Furthermore, given a finite system of equations over a torsion-free hyperbolic group $\Gamma$, there is an algorithm which constructs a canonical $Hom$-diagram and a complete set of induced $\Gamma$-NTQ systems, for $\Gamma_{R(S)}$. Finally, the class of $\Gamma$-limit groups is the same as that of iterated generalized doubles over $\Gamma$.

Included in

Mathematics Commons

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