Volume 9, issue 3 (2009)

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Quillen's plus construction and the D(2) problem

W H Mannan

Algebraic & Geometric Topology 9 (2009) 1399–1411
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.

Keywords
D2 problem, Quillen plus construction
Mathematical Subject Classification 2000
Primary: 57M20
Secondary: 19D06, 57M05