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Journals and Conferences
ABSTRACT We generalize some aspects of standard knot-theory to all ribbon-disc complements. We study asphericity of the complement of properly embedded links in certain contractible singular 3-manifolds that should be thought off as replacements of the 3-ball in the classical setting. We apply our results to show asphericity of 2-complexes modelled on… (More)
This paper is concerned with the homotopy type distinction of finite CW-complexes. A (G,n)-complex is a finite n-dimensional CW-complex with fundamental-group G and vanishing higher homotopy-groups up to dimension n − 1. In case G is an n-dimensional group there is a unique (up to homotopy) (G,n)-complex on the minimal Euler-characteristic level χmin(G,n).… (More)
We show that for finitely generated groups G with solvable word problem, there is no algorithm to determine whether H1(G) is trivial, nor whether H2(G) is trivial.
The Σ3-conjecture for metabelian groups is proved in the split extension case.
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 show that any finitely generated metabelian group can be embedded in a metabelian group of type F3. 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 F3 embedding theorem follows from… (More)
We show that the fundamental group of a ribbon disc complement in the four ball associated with certain prime dense and alternating surface arc projections are CAT(0) and δ-hyperbolic. Using this we produce an infinite class of free-by-cyclic CAT(0), δ-hyperbolic multi ribbon disc groups. AMS Subject classification: 57M05, 57M50, 20F65, 20F67.
We show that the fundamental group of a prime alternating surfacearc complement is δ-hyperbolic in case the genus of the surface is greater than zero. AMS Subject classification: 57M25, 57M50, 57M05
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 , 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)
Knot complements are aspherical. Whether this extends to ribbon disc complements, or, equivalently, to standard 2-complexes of labeled oriented trees, remains unresolved. It is known that prime injective labeled oriented trees are diagragramtically reducible, that is, aspherical in a strong combinatorial sense. We show that arbitrary prime labeled oriented… (More)