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

2022/10/24 by Harris Leung, Leung, Harris, Jeroen Schillewaert +3
Mathematics · #Advanced Topology and Set Theory #Fixed Point Theorems Analysis #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.2210.12951

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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