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ON ALGEBRAIC AND GEOMETRIC DIMENSIONS FOR GROUPS WITH TORSION

Published online by Cambridge University Press:  30 October 2001

NOEL BRADY ,
IAN J. LEARY  and
BRITA E. A. NUCINKIS
NOEL BRADY
Affiliation:
Department of Mathematics, University of Oklahoma, Norman, OK 73019, USA; nbrady@math.ou.edu
IAN J. LEARY
Affiliation:
Faculty of Mathematical Studies, University of Southampton, Southampton SO17 1BJ; ijl@maths.soton.ac.uk, bean@maths.soton.ac.uk
BRITA E. A. NUCINKIS
Affiliation:
Faculty of Mathematical Studies, University of Southampton, Southampton SO17 1BJ; ijl@maths.soton.ac.uk, bean@maths.soton.ac.uk Current address: Department of Mathematics, Eidgenössische Technische, Hochschule, Zürich CH-8092, Switzerland; bean@math.ethz.ch
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Abstract

Various notions of dimension for discrete groups are compared. A group is exhibited that acts with finite stabilizers on an acyclic 2-complex in such a way that the fixed point subcomplex for any non-trivial finite subgroup is contractible, but such that the group does not admit any such action on a contractible 2-complex. This group affords a counterexample to a natural generalization of the Eilenberg–Ganea conjecture.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 64 , Issue 2 , October 2001 , pp. 489 - 500
Copyright
The London Mathematical Society 2001

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