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We show that for finitely generated groups G with solvable word problem, there is no algorithm to determine whether H 1 (G) is trivial, nor whether H 2 (G) is trivial.
The Σ 3-conjecture for metabelian groups is proved in the split extension case.
We show that any finitely generated metabelian group can be embedded in a metabelian group of type F 3. More generally, we prove that if n is a positive integer and Q is a finitely generated abelian group, then any finitely generated ZQ-module can be embedded in a module that is n-tame. Combining with standard facts, the F 3 embedding theorem follows from… (More)
The following individuals read and discussed the thesis submitted by student Bailey Ann Ross, and they evaluated her presentation and response to questions during the final oral examination. They found that the student passed the final oral examination. ABSTRACT The genus of a graph is the minimal genus of a surface into which the graph can be embedded.… (More)
A labeled oriented tree is called injective, if each vertex occurs at most once as an edge label. We show that injective labeled oriented trees are aspherical. The proof uses a new relative asphericity test based on a lemma of Stallings.
Using stably free non-free relation modules we construct an infinite collection of 2–dimensional homotopy types, each of Euler-characteristic one and with trefoil fundamental group. This provides an affirmative answer to a question asked by Berridge and Dunwoody . We also give new examples of exotic relation modules. We show that the relation module… (More)
We construct infinitely many chain homotopically distinct algebraic 2-complexes for the Klein bottle group and give various topological applications. We compare our examples to other examples in the literature and address the question of geometric realizability.
We show that any finitely generated metabelian group can be embedded in a metabelian group of type F 3. The proof builds upon work of G. Baumslag , who independently with V. R. Remeslennikov  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.… (More)