Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)We show that limit groups are free-by-(torsion-free nilpotent) and have non-positive Euler characteristic. We prove that for any non-abelian limit group the Bieri-Neumann-Strebel-Renz S-invariants are the empty set. Let s >= 3 be a natural number and G be a subdirect product of non-abelian limit groups intersecting each factor non-trivially. We show that the homology groups of any subgroup of finite index in G, in dimension i <= s and with coefficients in Q, are finite-dimensional if and only if the projection of G to the direct product of any s of the limit groups has finite index. The case s 2 is a deep result of M. Bridson, J. Howie, C. F. Miller III and H. Short.o TEXTO COMPLETO DESTE ARTIGO, ESTARÁ DISPONÍVEL À PARTIR DE AGOSTO DE 2015.131119Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)