The D(2) property for D8

Mannan, W H

doi:10.2140/agt.2007.7.517

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The $D(2)$ property for $D_8$

W H Mannan

Algebraic & Geometric Topology 7 (2007) 517–528

DOI: 10.2140/agt.2007.7.517

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 $2^{n}$ and give a complete solution for the case where it is $D_{8}$ 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

Volume 7, issue 1 (2007)