Normal subgroups in duality groups and in groups of cohomological dimension 2

  title={Normal subgroups in duality groups and in groups of cohomological dimension 2},
  author={Robert B Bieri},
  journal={Journal of Pure and Applied Algebra},
  • R. Bieri
  • Published 1976
  • Mathematics
  • Journal of Pure and Applied Algebra

Arrangements of hypersurfaces and Bestvina–Brady groups

We show that quasi-projective Bestvina-Brady groups are fundamental groups of complements to hyperplane arrangements. Furthermore we relate other normal subgroups of right-angled Artin groups to

Dehn functions and finiteness properties of subgroups of perturbed right-angled Artin groups

We introduce the class of perturbed right-angled Artin groups. These are constructed by gluing Bieri double groups into standard right-angled Artin groups. As a first application of this construction

Normal subgroups of SimpHAtic groups

A group is SimpHAtic if it acts geometrically on a simply connected simplicially hereditarily aspherical (SimpHAtic) complex. We show that finitely presented normal subgroups of the SimpHAtic groups

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Let M be a 4‐manifold with residually finite fundamental group G having b1(G) > 0. Assume that M carries a symplectic structure with trivial canonical class K=0∈H2(M). Using a theorem of Bauer and

Toric complexes and Artin kernels

Normal Subgroups of Profinite Groups of Finite Cohomological Dimension

A profinite group G of finite cohomological dimension with (topologically) finitely generated closed normal subgroup N is studied. If G is pro‐p and N is either free as a pro‐p group or a Poincaré

Non-Positive Curvature and Group Theory

We have already seen that one can say a good deal about the structure of groups which act properly by isometries on CAT(0) spaces, particularly if the action is cocompact. One of the main goals of

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Cobordism for Poincaré duality groups

1. Relative homology for pairs. Homology and cohomology for a pair of groups G D S (cf. [6] ) can be extended to pairs (G, S) consisting of a group G and a family of subgroups S = {St}, as follows:



An Improved Subgroup Theorem for HNN Groups with Some Applications

In [4], a subgroup theorem for HNN groups was established. The theorem was proved by embedding the given HNN group in a free product with amalgamated subgroup and then applying the subgroup theorem


In the paper we calculate the weak dimension of the group algebra of a solvable group and the projective dimension of the group algebra of a countable nilpotent group. Exact bounds are obtained for