On the semisimplicity of polyhedral isometries

Author:

Bridson Martin

Abstract

If a polyhedral complex K K has only finitely many isometry types of cells, then all of its cellular isometries are semisimple. If K K is 1-connected and non-positively curved, then any solvable group that acts freely by cellular isometries on K K is finitely generated and contains an abelian subgroup of finite index.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

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5. Some relations between the metric structure and the algebraic structure of the fundamental group in manifolds of nonpositive curvature;Gromoll, Detlef;Bull. Amer. Math. Soc.,1971

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