Algebraic & Geometric Topology

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

W H Mannan

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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.

Article information

Algebr. Geom. Topol., Volume 9, Number 3 (2009), 1399-1411.

Received: 21 May 2008
Revised: 21 February 2009
Accepted: 9 June 2009
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M20: Two-dimensional complexes
Secondary: 19D06: $Q$- and plus-constructions 57M05: Fundamental group, presentations, free differential calculus

D2 problem Quillen plus construction


Mannan, W H. Quillen's plus construction and the D(2) problem. Algebr. Geom. Topol. 9 (2009), no. 3, 1399--1411. doi:10.2140/agt.2009.9.1399.

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