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

Published 24 Oct 2022 in math.GR and math.MG | (2210.12951v1)

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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