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

@article{Bieri1976NormalSI, title={Normal subgroups in duality groups and in groups of cohomological dimension 2}, author={Robert B Bieri}, journal={Journal of Pure and Applied Algebra}, year={1976}, volume={7}, pages={35-51} }

## 80 Citations

### Arrangements of hypersurfaces and Bestvina–Brady groups

- Mathematics
- 2015

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

- Mathematics
- 2011

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

- MathematicsJournal of Topology and Analysis
- 2021

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…

### On the topology of symplectic Calabi–Yau 4‐manifolds

- Mathematics
- 2012

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…

### Normal Subgroups of Profinite Groups of Finite Cohomological Dimension

- Mathematics
- 2004

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

- Mathematics
- 1999

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…

### Cobordism for Poincaré duality groups

- Mathematics
- 1976

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:…

## References

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- MathematicsCanadian Journal of Mathematics
- 1974

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…

### A FINITELY PRESENTED GROUP WHOSE 3-DIMENSIONAL INTEGRAL HOMOLOGY IS NOT FINITELY GENERArED.*

- Mathematics
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### ON THE HOMOLOGICAL DIMENSION OF GROUP ALGEBRAS OF SOLVABLE GROUPS

- Mathematics
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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…