We prove the equivalence of several sets of axioms for non-discrete affine buildings, by
providing different types of metric, exchange and atlas conditions. We apply our result to …

In this work we describe horofunction compactifications of metric spaces and finite-
dimensional real vector spaces through asymmetric metrics and asymmetric polyhedral …

The character variety, which parametrizes reductive representations of finitely generated
groups in $\mathrm {PSL} _2 (\mathbb {R}) $, has many compactifications. We construct a …

We develop the theory of algebraic groups over real closed fields and apply the results to
construct a geometric object $\mathcal {B} $ and to prove that $\mathcal {B} $ is an affine …

We prove the following rigidity results. Coarse equivalences between metrically complete
Euclidean buildings preserve spherical buildings at infinity. If all irreducible factors have …

In this two-part paper we prove an existence result for affine buildings arising from
exceptional algebraic reductive groups. Combined with earlier results on classical groups …

Let $\mathbf {G} $ be a quasi-split reductive group and $\mathbb {K} $ be a Henselian field
equipped with a valuation $\omega:\mathbb {K}^{\times}\rightarrow\Lambda $, where …

Let G be a semi-simple Lie group without compact factors, and consider a maximal compact
subgroup K in G. For example, we could take G= SLn (R) and K= SOn (R). The …

Axioms of affine buildings Page 1 . AXIOMS OF AFFINE BUILDINGS PETRA N. SCHWER (NÉE
HITZELBERGER) Abstract. We prove equivalence of certain axiom sets for a ne buildings …

We prove equivalence of certain reduced axiom sets for generalized affine buildings. Our
results extend the work of Anne Parreau. Further we give a purely combinatorial proof of the …