Related papers: The flat closing problem for buildings

We classify compact complex surfaces whose groups of bimeromorphic selfmaps have bounded finite subgroups. We also prove that the stabilizer of a point in the automorphism group of a compact complex surface of zero Kodaira dimension, as…

We study algebraic properties on a group G such that if the discrete group G has these properties then every locally compact shift continuous topology on G with adjoined zero is either compact, or discrete. We introduce electorally flexible…

Let $\Delta$ be a locally finite thick building of type $\tilde{A}_2$. We show that, if the type-preserving automorphism group $\mathrm{Aut}(\Delta)^+$ of $\Delta$ is transitive on panels of each type, then either $\Delta$ is Bruhat--Tits…

Despite the significance of the notion of parabolic closures in Coxeter groups of finite ranks, the parabolic closure is not guaranteed to exist as a parabolic subgroup in a general case. In this paper, first we give a concrete example to…

This (quasi-)survey addresses the quasi-isometry classification of locally compact groups, with an emphasis on amenable hyperbolic locally compact groups. This encompasses the problem of quasi-isometry classification of homogeneous…

We show that for any closed surface of genus greater than one and for any finite weighted graph filling the surface, there exists a hyperbolic metric which realizes the least Dirichlet energy harmonic embedding of the graph among a fixed…

We prove that the outer automorphism group $Out(G)$ is residually finite when the group $G$ is virtually compact special (in the sense of Haglund and Wise) or when $G$ is isomorphic to the fundamental group of some compact $3$-manifold. To…

We consider finite 2-complexes X that arise as quotients of Fuchsian buildings by subgroups of the combinatorial automorphism group, which we assume act freely and cocompactly. We show that locally CAT(-1) metrics on X which are piecewise…

We study the general form of isomorphisms on the algebra of compactly supported complex-valued continuous functions defined on a locally compact Hausdorff space (the proof of which works for the algebra of $C^k-$differentiable functions on…

We give a complete characterization of the locally compact groups that are non-elementary Gromov-hyperbolic and amenable. They coincide with the class of mapping tori of discrete or continuous one-parameter groups of compacting…

We prove that if an asymptotically Schwarzschildean 3-manifold (M,g) contains a properly embedded stable minimal surface, then it is isometric to the Euclidean space. This implies, for instance, that in presence of a positive ADM mass any…

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 on finite rank buildings with measurable…

We prove that every 2-local automorphism of the unitary group or the general linear group on a complex infinite-dimensional separable Hilbert space is an automorphism. Thus these types of transformations are completely determined by their…

Given a split semisimple group over a local field, we consider the maximal Satake-Berkovich compactification of the corresponding Euclidean building. We prove that it can be equivariantly identified with the compactification which we get by…

In this paper, we extend the concept of generalized entropy to uniform spaces, allowing computations beyond metrizable settings. We apply this to parabolic dynamics - systems with a unique fixed point uniformly attracting all compact…

An automorphism of a spherical building is called \textit{domestic} if it maps no chamber onto an opposite chamber. This paper forms a significant part of a large project classifying domestic automorphisms of spherical buildings of…

In the last years, there has been a large amount of research on embeddability properties of finitely generated hyperbolic groups. In this paper, we elaborate on the more general class of locally compact hyperbolic groups. We compute the…

We propose methods towards a systematic determination of d dimensional curved spaces where Euclidean field theories with rigid supersymmetry can be defined. The analysis is carried out from a group theory as well as from a supergravity…

Let $\Gamma$ be a graph product of finite groups, with finite underlying graph, and let $\Delta$ be the associated right-angled building. We prove that a uniform lattice $\Lambda$ in the cubical automorphism group Aut$(\Delta)$ is weakly…

Every transformation monoid comes equipped with a canonical topology-the topology of pointwise convergence. For some structures, the topology of the endomorphism monoid can be reconstructed from its underlying abstract monoid. This…