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Mostow rigidity for Fuchsian buildings

Xiangdong Xie
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Abstract

We show that if a homeomorphism between the ideal boundaries of two Fuchsian buildings preserves the combinatorial cross ratio almost everywhere, then it extends to an isomorphism between the Fuchsian buildings. It follows that Mostow rigidity holds for Fuchsian buildings: if a group acts properly and cocompactly on two Fuchsian buildings X and Y, then X and Y are equivariantly isomorphic.

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Xiangdong Xie. 2004-07-23. Mostow rigidity for Fuchsian buildings. https://arxiv.org/abs/math/0407394

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