On the semisimplicity of polyhedral isometries

Bridson, Martin

doi:10.1090/S0002-9939-99-05187-4

On the semisimplicity of polyhedral isometries
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by Martin R. Bridson

Proc. Amer. Math. Soc. 127 (1999), 2143-2146

DOI: https://doi.org/10.1090/S0002-9939-99-05187-4

Published electronically: March 16, 1999

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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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