English

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 A~2\tilde{A}_2 or C~2\tilde{C}_2. In the discrete case, our theorem establishes the corresponding special cases of a conjecture by Marquis.

Keywords

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

R2 v1 2026-06-23T13:59:47.763Z