Fixed points for group actions on 2-dimensional affine buildings
Group Theory
2022-12-07 v3 Metric Geometry
Abstract
We prove a local-to-global result for fixed points of groups acting on affine buildings (possibly non-discrete) of types or . In the discrete case, our theorem establishes the corresponding special cases of a conjecture by Marquis.
Cite
@article{arxiv.2003.00681,
title = {Fixed points for group actions on 2-dimensional affine buildings},
author = {Jeroen Schillewaert and Koen Struyve and Anne Thomas},
journal= {arXiv preprint arXiv:2003.00681},
year = {2022}
}
Comments
Substantial revision, generalised Busemann function argument to CAT(0) spaces, streamlined some other proofs and added explanation why our method does not seem to work for the $\tilde{G}_2$case