Related papers: The cone topology on masures

A hovel is a generalization of the Bruhat-Tits building that is associated to an almost split Kac-Moody group G over a non-Archimedean local field. In particular, G acts strongly transitively on its corresponding hovel $\Delta$ as well as…

Let $\mathfrak{G}$ be a split reductive group, $\mathbb{k}$ be a field and $\varpi$ be an indeterminate. In order to study $\mathfrak{G}(\mathbb{k}[\varpi,\varpi^{-1}])$ and $\mathfrak{G}(\mathbb{k}(\varpi))$, one can make them act on their…

Masures are generalizations of Bruhat-Tits buildings. They were introduced to study Kac-Moody groups over ultrametric fields, which generalize reductive groups over the same fields. If A and A are two apartments in a building, their…

Firstly, we prove that every closed subgroup $H$ of type-preserving automorphisms of a locally finite thick affine building $\Delta$ of dimension $\geq 2$ that acts strongly transitively on $\Delta$ is Moufang. If moreover $\Delta$ is…

We prove a decomposition result for a group $G$ acting strongly transitively on the Tits boundary of a Euclidean building. As an application we provide a local to global result for discrete Euclidean buildings, which generalizes results in…

Masures are generalizations of Bruhat-Tits buildings. They were introduced by Gaussent and Rousseau in order to study Kac-Moody groups over valued fields. We prove that the intersection of two apartments of a masure is convex. Using this,…

Masures are generalizations of Bruhat-Tits buildings adapted to the study of Kac--Moody groups over valued fields. They were introduced by Gaussent and Rousseau in 2007. Rousseau defined an axiomatic for these object and we simplified it.…

Let G be a locally compact group acting properly by type-preserving automorphisms on a locally finite thick Euclidean building $\Delta$ and K be the stabilizer of a special vertex in $\Delta$. It is known that (G, K) is a Gelfand pair as…

Topological T-duality is a transformation taking a gerbe on a principal torus bundle to a gerbe on a principal dual-torus bundle. We give a new geometric construction of T-dualization, which allows the duality to be extended in following…

We study two transitivity properties for group actions on buildings, called Weyl transitivity and strong transitivity. Following hints by Tits, we give examples involving anisotropic algebraic groups to show that strong transitivity is…

We study universal groups for right-angled buildings. Inspired by Simon Smith's work on universal groups for trees, we explicitly allow local groups that are not necessarily finite nor transitive. We discuss various topological and…

Sublinearly Morse boundaries of proper geodesic spaces are introduced by Qing, Rafi and Tiozzo. Expanding on this work, Qing and Rafi recently developed the quasi-redirecting boundary, denoted $\partial G$, to include all directions of…

Transformation groupoids associated to group actions capture the interplay between global and local symmetries of structures described in set-theoretic terms. This paper examines the analogous situation for structures described in…

Kac-Moody groups over finite fields are finitely generated groups. Most of them can naturally be viewed as irreducible lattices in products of two closed automorphism groups of non-positively curved twinned buildings: those are the most…

In this paper, we study the uniformities on the double coset spaces in topological groups. As an implication, the quotient spaces of topological groups with a $q$-point are studied. It mainly shows that: (1) Suppose that $G$ is a…

Some basic notions and results in Topological Dynamics are extended to continuous groupoid actions in topological spaces. We focus mainly on recurrence properties. Besides results that are analogous to the classical case of group actions,…

This is the second of two papers but has been written so as to have minimal dependence on the first paper (which is also on this archive). Let G be a group and let M be a CAT(0) proper metric space (e.g. a simply connected complete…

Let $G$ be a group with a non-elementary action on a (not necessarily discrete) $\tilde{A}_2$-buildings. We prove that, given a random walk on $G$, isometries in $G$ are strongly regular hyperbolic with high probability. As a consequence,…

In this article we study the transitivity of the group of automorphisms of real algebraic surfaces. We characterize real algebraic surfaces with very transitive automorphism groups. We give applications to the classification of real…

We described in [M1] a monoid acting on the integrable highest weight modules of a symmetrizable Kac-Moody algebra. It has similar structural properties as a reductive algebraic monoid with unit group a Kac-Moody group. Now we find natural…