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The geodesic flow of a nonpositively curved graph manifold

Christopher B. Croke·Bruce Kleiner
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Abstract

We study discrete, cocompact, isometric actions of groups on Hadamard spaces, and the induced actions on ideal boundaries. For a class of groups generalizing fundamental groups of three-dimensional graph manifolds, we find a set of invariants for the action which determine the boundary action up to equivariant homeomorphism. This work was inspired by (and answers) a question of Gromov from "Asymptotic invariants of infinite groups."

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Christopher B. Croke, Bruce Kleiner. 1999-11-22. The geodesic flow of a nonpositively curved graph manifold. https://arxiv.org/abs/math/9911170

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