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- Jens Harlander, STEPHAN ROSEBROCK, S. Rosebrock
- 2003

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)

- William A. Bogley, Jens Harlander
- IJAC
- 2002

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 [1]. 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)

- Jens Harlander
- 2008

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.

- Jens Harlander
- 2008

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 [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.… (More)

- Jens Harlander, Stephan Rosebrock
- 2011

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)