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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 Ω3() 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
References
Publication
Received: 26 May 2013
Revised: 6 June 2013
Accepted: 11 June 2013
Published: 10 October 2013
Authors
Wajid H Mannan
Mathematics and Statistics
Lancaster University
Lancaster LA1 4YF
UK
http://www.lancs.ac.uk/fas/maths/people/wajid-mannan
Seamus O’Shea
Department of Mathematics
University College London
Gower Street
London WC1E 6BT
UK