منابع مشابه
Homological and Finiteness Properties of Picture Groups
Picture groups are a class of groups introduced by Guba and Sapir. Known examples include Thompson’s groups F , T , and V . In this paper, a large class of picture groups is proved to be of type F∞. A Morse-theoretic argument shows that, for a given picture group, the rational homology vanishes in almost all dimensions.
متن کاملJumping loci and finiteness properties of groups
Characteristic varieties. Let X be a connected CW-complex with finitely many cells in each dimension, and G its fundamental group. The characteristic varieties of X are the jumping loci for cohomology with coefficients in rank 1 local systems: V i k (X) = {ρ ∈ Hom(G,C∗) | dimH(X,Cρ) ≥ k}. These varieties emerged from the work of Novikov [22] on Morse theory for closed 1-forms on manifolds. It t...
متن کاملImproving Finiteness Properties for Metabelian Groups
We show that any finitely generated metabelian group can be embedded in a metabelian group of type F3. The proof builds upon work of G. Baumslag [4], who independently with V. R. Remeslennikov [10] proved that any finitely generated metabelian group can be embedded in a finitely presented one. We also rely essentially on the Sigma theory of R. Bieri and R. Strebel [7], who introduced this geome...
متن کاملStructure and Finiteness Properties of Subdirect Products of Groups
We investigate the structure of subdirect products of groups, particularly their finiteness properties. We pay special attention to the subdirect products of free groups, surface groups and HNN extensions. We prove that a finitely presented subdirect product of free and surface groups virtually contains a term of the lower central series of the direct product or else fails to intersect one of t...
متن کاملFiniteness Properties of Some Groups of Local Similarities
Hughes has defined a class of groups, which we call FSS (finite similarity structure) groups. Each FSS group acts on a compact ultrametric space by local similarities. The best-known example is Thompson’s group V . Guided by previous work on Thompson’s group V , we establish a number of new results about FSS groups. Our main result is that a class of FSS groups are of type F∞. This generalizes ...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 1987
ISSN: 0022-4049
DOI: 10.1016/0022-4049(87)90015-6