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- Larsen Louder
- 2008

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 boundedâ€¦ (More)

- Larsen Louder, LARS LOUDER
- 2009

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 seriesâ€¦ (More)

- Larsen Louder, LARS LOUDER
- 2008

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 toâ€¦ (More)

- Larsen Louder, ChloÃ© Perin, Rizos Sklinos
- Notre Dame Journal of Formal Logic
- 2013

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 theâ€¦ (More)

- Larsen Louder
- 2008

We prove a number of generalizations of the fact that any homomorphism of a nonorientable surface group with Euler characteristic âˆ’1 to a free group has cyclic image. This is important for our workâ€¦ (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 BÄ™dlewo, Poland in July 2005.

- Larsen Louder
- 2008

It is shown that strict resolutions of Fn by Fâ€“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).

- Larsen Louder, D. B. McReynolds, Brandy M McReynolds, Ben Klaff
- 2009

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 minorâ€¦ (More)

- Larsen Louder
- 2008

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 groupâ€¦ (More)

- Larsen Louder
- 2006

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 aâ€¦ (More)