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

We prove that if two finitely generated groups act by isometries 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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Keywords

Euclidean buildings, fixed point sets, distance

Mathematical Subject Classification

Primary: 20E42

Milestones

Received: 23 October 2022

Revised: 26 June 2023

Accepted: 17 July 2023

Published: 13 September 2023

Authors

Harris Leung
University of Auckland Auckland New Zealand

Jeroen Schillewaert
University of Auckland Auckland New Zealand

Anne Thomas
School of Mathematics and Statistics University of Sydney Sydney Australia

Vol. 20, No. 2-3, 2023

Harris Leung, Jeroen Schillewaert and Anne Thomas

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification

Milestones

Authors