Volume 13, issue 6 (2013)

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Minimal algebraic complexes over $D_{4n}$

Wajid H Mannan and Seamus O’Shea

Algebraic & Geometric Topology 13 (2013) 3287–3304
Abstract

We show that cancellation of free modules holds in the stable class ${\Omega }_{3}\left(ℤ\right)$ 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 dihedral groups satisfy the D(2) property.

Keywords
non-simply connected homotopy, cancellation of modules, Wall's D(2) problem, algebraic homotopy
Mathematical Subject Classification 2010
Primary: 57M20
Secondary: 16E05, 16E10, 55P15, 55Q20