Volume 7, issue 1 (2007)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
The $D(2)$ property for $D_8$

W H Mannan

Algebraic & Geometric Topology 7 (2007) 517–528
Abstract

Wall’s D(2) problem asks if a cohomologically 2–dimensional geometric 3–complex is necessarily homotopy equivalent to a geometric 2–complex. We solve part of the problem when the fundamental group is dihedral of order 2n and give a complete solution for the case where it is D8 the dihedral group of order 8.

Keywords
Wall's D(2) problem, algebraic complexes, k-invariants
Mathematical Subject Classification 2000
Primary: 57M20
Secondary: 57M05
References
Publication
Received: 4 October 2006
Revised: 10 February 2007
Accepted: 10 February 2007
Published: 25 April 2007
Authors
W H Mannan
University College London
Gower Street
London WC1E 6BT
UK