Hostname: page-component-7d8f8d645b-xmxxh Total loading time: 0 Render date: 2023-05-27T21:47:48.912Z Has data issue: false Feature Flags: { "useRatesEcommerce": true } hasContentIssue false

Realizing algebraic 2-complexes by cell complexes

Published online by Cambridge University Press:  01 May 2009

Department of Pure Mathematics, University of Sheffield, Hounsfield Road, Sheffield S3 7RH e-mail:


The realization theorem asserts that for a finitely presented group G, the D(2) property and the realization property are equivalent as long as G satisfies a certain finiteness condition. We show that the two properties are in fact equivalent for all finitely presented groups.

Research Article
Copyright © Cambridge Philosophical Society 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)



[1]Johnson, F. E. A.Stable Modules and the D(2) Problem. LMS Lecture Note Series 301 (Cambridge University Press, 2003).CrossRefGoogle Scholar
[2]Mannan, W. H.Homotopy types of truncated projective resolutions. Homology, Homotopy and Applications 9 (2) (2007), 445449.CrossRefGoogle Scholar
[3]Stallings, J. R.On torsion free groups with infinitely many ends. Ann. of Math. 2nd Series 88 (1968), 312334.CrossRefGoogle Scholar
[4]Swan, R. G.Groups of cohomological dimension one. J. Algebra 12 (1969), 585610.CrossRefGoogle Scholar
[5]Wall, C. T. C.Finiteness conditions for CW–complexes. Ann. of Math. 81 (1965), 5669.CrossRefGoogle Scholar