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

Mannan, W H

doi:10.2140/agt.2009.9.1399

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

W H Mannan

Algebraic & Geometric Topology 9 (2009) 1399–1411

DOI: 10.2140/agt.2009.9.1399

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

References

Publication

Received: 21 May 2008

Revised: 21 February 2009

Accepted: 9 June 2009

Published: 5 July 2009

Authors

W H Mannan
Building 54 School of Mathematics University of Southampton University Road Southampton SO17 1BJ United Kingdom

Volume 9, issue 3 (2009)