Minimal algebraic complexes over D4n

Mannan, Wajid H; O’Shea, Seamus

doi:10.2140/agt.2013.13.3287

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Minimal algebraic complexes over $D_{4n}$

Wajid H Mannan and Seamus O’Shea

Algebraic & Geometric Topology 13 (2013) 3287–3304

DOI: 10.2140/agt.2013.13.3287

Abstract

We show that cancellation of free modules holds in the stable class $Ω_{3} (ℤ)$ over dihedral groups of order $4 n$ . 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

Volume 13, issue 6 (2013)