Minimal algebraic complexes over $D_{4n}$

Abstract

We show that cancellation of free modules holds in the stable class ${\Omega }_3(\mathbb{Z})$ over dihedral groups of order $4n$. In light of a recent result on realizing $k$-invariants for these groups, this completes the proof that all all dihedral groups satisfy the D(2) property.

arXiv commentPaper published in peer reviewed journal in 2013

References in corpus (7)

• Realizing algebraic 2-complexes by cell complexes
• Deficiency and abelianized deficiency of some virtually free groups
• The D(2) property for $D_8$
• Quillen's Plus Construction and the D(2) problem
• Generalised Swan modules and the D(2) problem
• Homotopy types of truncated projective resolutions
• Periodic cohomology

Cited by in corpus (4)

• Two remarks on Wall's D2 problem
• An exotic presentation of Q_28
• Homotopy classification of 4-manifolds whose fundamental group is dihedral
• On Homology Roses and the D(2)-problem