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On the semisimplicity of polyhedral isometries


Author: Martin R. Bridson
Journal: Proc. Amer. Math. Soc. 127 (1999), 2143-2146
MSC (1991): Primary 53C23, 20F32
DOI: https://doi.org/10.1090/S0002-9939-99-05187-4
Published electronically: March 16, 1999
MathSciNet review: 1646316
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Abstract: If a polyhedral complex $K$ has only finitely many isometry types of cells, then all of its cellular isometries are semisimple. If $K$ is 1-connected and non-positively curved, then any solvable group that acts freely by cellular isometries on $K$ is finitely generated and contains an abelian subgroup of finite index.


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Additional Information

Martin R. Bridson
Affiliation: Mathematical Institute, 24–29 St Giles’, Oxford, OX1 3LB, United Kingdom
Email: bridson@maths.ox.ac.uk

DOI: https://doi.org/10.1090/S0002-9939-99-05187-4
Keywords: Non-positive curvature, semisimple isometries
Received by editor(s): October 7, 1997
Published electronically: March 16, 1999
Additional Notes: This work was supported by an EPSRC Advanced Fellowship, NSF grant 9401362 and the British Council
Communicated by: Ronald M. Solomon
Article copyright: © Copyright 1999 American Mathematical Society

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