Distances between fixed-point sets in 2-dimensional Euclidean buildings are realised
Group Theory
2022-10-25 v1 Metric Geometry
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.
Cite
@article{arxiv.2210.12951,
title = {Distances between fixed-point sets in 2-dimensional Euclidean buildings are realised},
author = {Harris Leung and Jeroen Schillewaert and Anne Thomas},
journal= {arXiv preprint arXiv:2210.12951},
year = {2022}
}
Comments
8 pages