Krull dimension for limit groups I: Bounding strict resolutions

Larsen Louder

Published 2007-02-05, updated 2008-12-10Version 3

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 length. The upper bound plays two roles in our approach. First, it provides upper bounds for heights of analysis lattices of limit groups, and second, it enables the construction of \jsj--respecting sequences in the sequel.