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Combinatorial harmonic maps and discrete-group actions on Hadamard spaces

Hiroyasu Izeki·Shin Nayatani
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Abstract

We use the combinatorial harmonic map theory to study the isometric actions of discrete groups on Hadamard spaces. Given a finitely generated group acting by automorphisms, properly discontinuously and cofinitely on a simplicial complex and its isometric action on a Hadamard space, we formulate criterions for the action to have a global fixed point.

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Hiroyasu Izeki, Shin Nayatani. 2004-10-01. Combinatorial harmonic maps and discrete-group actions on Hadamard spaces. https://arxiv.org/abs/math/0410019

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