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.

Paper published in peer reviewed journal in 2013

References in corpus (3)

• Realizing algebraic 2-complexes by cell complexes
• The D(2) property for $D_8$
• Quillen's Plus Construction and the D(2) problem