• Corpus ID: 211678018

# Fixed points for group actions on 2-dimensional affine buildings

@article{Schillewaert2020FixedPF,
title={Fixed points for group actions on 2-dimensional affine buildings},
author={Jeroen Schillewaert and Koen Struyve and Anne Thomas},
journal={arXiv: Group Theory},
year={2020}
}
• Published 2 March 2020
• Mathematics
• arXiv: Group Theory
We prove a local-to-global result for fixed points of groups acting on affine buildings (possibly non-discrete) of types $\tilde{A}_1\times \tilde{A}_1, \tilde{A}_2$ or $\tilde{C}_2$. In the discrete case, our theorem establishes a conjecture by Marquis.

## References

SHOWING 1-10 OF 38 REFERENCES

We establish a fixed point property for a certain class of locally compact groups, including almost connected Lie groups and compact groups of finite abelian width, which act by simplicial isometries
We show, under mild hypotheses, that if each element of a finitely generated group acting on a 2-dimensional CAT(0) complex has a fixed point, then the action is trivial. In particular, all actions
We prove two generalizations of results proved by Bruhat and Tits involving metrical completeness and R-buildings. Firstly, we give a generalization of the Bruhat-Tits fixed point theorem also valid
• Mathematics
• 2010
We show that any filtering family of closed convex subsets of a finite-dimensional CAT(0) space X has a non-empty intersection in the visual bordification $${ \overline{X} = X \cup \partial X}$$ .
• Mathematics
• 2018
We deduce from Sageev's results that whenever a group acts locally elliptically on a finite dimensional CAT(0) cube complex, then it must fix a point. As an application, we give an example of a group
• Mathematics
• 1997
Abstract We study quasi-isometries between products of symmetric spaces and Euclidean buildings. The main results are that quasi-isometries preserve the product structure, and that in the irreducible
• Mathematics
• 2018
We recast the notion of joint spectral radius in the setting of groups acting by isometries on non-positively curved spaces and give geometric versions of results of Berger-Wang and Bochi valid for
• Mathematics
• 2004
A Tits alternative theorem is proved in this paper for groups acting on CAT(0) cubical complexes. That is, a proof is given to show that if G is assumed to be a group for which there is a bound on