Volume 12, issue 4 (2012)

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The $D(2)$–problem for dihedral groups of order $4n$

Seamus O’Shea

Algebraic & Geometric Topology 12 (2012) 2287–2297
Abstract

We give a full solution in terms of $k$–invariants of the $D\left(2\right)$–problem for ${D}_{4n}$, assuming that $\mathbf{Z}\left[{D}_{4n}\right]$ satisfies torsion-free cancellation.

Keywords
$D(2)$–problem, algebraic 2–complex, $k$–invariant
Primary: 57M05
Secondary: 55P15