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Journals and Conferences
This is the first paper in a sequence on Krull dimension for limit groups, answering a question of Z. Sela. In this paper we show that strict resolutions of a fixed limit group have uniformly bounded… (More)
Let L be a limit group. The Krull dimension of L is the supremum of lengths of chains of proper epimorphisms of limit groups originating from L. This is the third paper in a four part series series… (More)
This is the second paper in a sequence on Krull dimension for limit groups, answering a question of Z. Sela. In it we develop the notion of a resolution of a sequence of limit groups and show how to… (More)
We use hyperbolic towers to answer some model-theoretic questions around the generic type in the theory of free groups. We show that all the finitely generated models of this theory realize the… (More)
We prove a number of generalizations of the fact that any homomorphism of a nonorientable surface group with Euler characteristic −1 to a free group has cyclic image. This is important for our work… (More)
This survey was compiled from lectures and problem sessions at the International Conference on Geometric Topology at the Mathematical Research and Conference Center in Będlewo, Poland in July 2005.
It is shown that strict resolutions of Fn by F–limit groups have length bounded by 3n. As an application we show that the abelian analysis lattice of a limit group L has height bounded by 3 rk(L).
One purpose of this article is to investigate the interplay between the join and intersection of a pair of finitely generated subgroups of a free group. Our main result, Theorem 2.4, is a minor… (More)
This is the third paper in a sequence on Krull dimension for limit groups, answering a question of Z. Sela. We give generalizations of the well known fact that a nontrivial commutator in a free group… (More)
Several classical facts due to Lyndon, Shenitzer, and Baumslag about ranks of subgroups generated by solutions to equations over the free group are generalized and given a uniform proof. Given a… (More)