Quillen's Plus Construction and the D(2) problem

Abstract

Given a finite connected 3-complex with cohomological dimension 2, we show it may be constructed up to homotopy by applying the Quillen plus construction to the Cayley complex of a finite group presentation. This reduces the D(2) problem to a question about perfect normal subgroups.

Paper published in peer reviewed journal in 2009

References in corpus (1)

• The D(2) property for $D_8$

Cited by in corpus (2)

• Minimal algebraic complexes over $D_{4n}$
• Explicit generators for the relation module in the example of Gruenberg-Linnell