The D(2) property for D8

Abstract

Wall's D(2) problem asks if a cohomologically 2-dimensional geometric 3-complex is necessarily homotopy equivalent to a geometric 2-complex. W e 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 D8 the dihedral group of order 8. © 2007 Mathematical Sciences Publishers.