English

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.

Keywords

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

R2 v1 2026-06-28T04:19:20.149Z