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arXiv · 2210.12951

Distances between fixed-point sets in 2-dimensional Euclidean buildings are realised

Harris Leung·Jeroen Schillewaert·Anne Thomas
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Abstract

We prove that if two finitely generated groups act on a metrically complete 2-dimensional Euclidean building, then the distance between their fixed-point sets is realised. Our proof uses the geometry of Euclidean buildings, which we view as CAT(0) spaces, and properties of ultrapowers of Euclidean buildings.

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Harris Leung, Jeroen Schillewaert, Anne Thomas. 2022-10-24. Distances between fixed-point sets in 2-dimensional Euclidean buildings are realised. https://arxiv.org/abs/2210.12951

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