Geodesic
Diophantine geometry over groups I : Makanin-Razborov diagrams
Publications Mathématiques de l'IHÉS, Tome 93 (2001), pp. 31-105

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This paper is the first in a sequence 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 first paper we present the (canonical) Makanin-Razborov diagram that encodes the set of solutions of a system of equations. We continue by studying parametric families of sets of solutions, and associate with such a family a canonical graded Makanin-Razborov diagram, that encodes the collection of Makanin-Razborov diagrams associated with the individual members in the parametric family.

@article{PMIHES_2001__93__31_0,
     author = {Sela, Zlil},
     title = {Diophantine geometry over groups {I} : {Makanin-Razborov} diagrams},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {31--105},
     publisher = {Institut des Hautes \'Etudes Scientifiques},
     volume = {93},
     year = {2001},
     mrnumber = {1863735},
     zbl = {1018.20034},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PMIHES_2001__93__31_0/}
}
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Sela, Zlil. Diophantine geometry over groups I : Makanin-Razborov diagrams. Publications Mathématiques de l'IHÉS, Tome 93 (2001), pp. 31-105. http://geodesic.mathdoc.fr/item/PMIHES_2001__93__31_0/