#### Volume 7, issue 1 (2007)

 Recent Issues
 The Journal About the Journal Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Subscriptions Author Index To Appear Contacts 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 $D\left(2\right)$ 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
Primary: 57M20
Secondary: 57M05