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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Minimal 2-complexes and the D(2)-problem


Author: F. E. A. Johnson
Journal: Proc. Amer. Math. Soc. 132 (2004), 579-586
MSC (2000): Primary 55M05, 57M20; Secondary 16D70
Published electronically: September 5, 2003
MathSciNet review: 2022384
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Abstract: We show that when $n\geq 5$ there is a minimal algebraic $2$-complex over the quaternion group $Q(2^n)$ which is not homotopy equivalent to the Cayley complex of the standard minimal presentation. This raises the possibility that Wall's D(2)-property might fail for $Q(2^n)$.


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Additional Information

F. E. A. Johnson
Affiliation: Department of Mathematics, University College London, Gower Street, London WC1E 6BT, United Kingdom
Email: feaj@math.ucl.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07068-0
PII: S 0002-9939(03)07068-0
Keywords: Algebraic $2$-complexes, non-cancellation, minimal presentations
Received by editor(s): December 28, 2000
Received by editor(s) in revised form: August 22, 2002
Published electronically: September 5, 2003
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 2003 American Mathematical Society