Related papers: Tits Geometry and Positive Curvature

We announce a generalization of Zimmer's cocycle superrigidity theorem proven using harmonic map techniques. This allows us to generalize many results concerning higher rank lattices to all lattices in semisimple groups with property $(T)$.…

Answering a problem posed by the second author on Mathoverflow, we prove that the connected countable Hausdorff spaces constructed by Bing and Ritter are topologically homogeneous.

A generalized-homology bordism-theory is constructed, such that for certain manifold homotopy stratified sets (MHSS; Quinn-spaces) homeomorphism-invariant geometric fundamental-classes exist. The construction combines three ideas: Firstly,…

We study the basic properties of a dual "spectral" topology on positive type spaces of h-inductive theories and its essential connection to infinitary logic. The topology is Hausdorff, has the Baire property, and its compactness…

We study uniformization problems for compact manifolds that arise as quotients of domains in complex flag varieties by images of Anosov homomorphisms. We focus on Anosov homomorphisms with "small" limit sets, as measured by the Riemannian…

We investigate the Tits buildings of the paramodular groups with or without canonical level structure, respectively. These give important combinatorical information about the boundary of the toroidal compactification of the moduli spaces of…

We already saw in [A1] that the space of dynamically marked rational maps can be identified to a subspace of the space of covers between trees of spheres on which there is a notion of convergence that makes it sequentially compact. In the…

Let $M_\Sigma$ be an $n$-dimensional Thom-Mather stratified space of depth $1$. We denote by $\beta M$ the singular locus and by $L$ the associated link. In this paper we study the problem of when such a space can be endowed with a wedge…

We show that every subgroup of the mapping class group MCG(S) of a compact surface S is either virtually abelian or it has infinite dimensional second bounded cohomology. As an application, we give another proof of the…

We obtain new invariants of topological link concordance and homology cobordism of 3-manifolds from Hirzebruch-type intersection form defects of towers of iterated p-covers. Our invariants can extract geometric information from an arbitrary…

This paper is about geometric and topological properties of a proper CAT(0) space $X$ which is cocompact - i.e. which has a compact generating domain with respect to the full isometry group. It is shown that geodesic segments in $X$ can…

Inspired by the Bruhat-Tits building of SL$_n$($\mathbb Q_p$), we construct a complete metric space X with an action of the tame automorphism group of the affine space Tame($K^n$). The points in X are certain monomial valuations, and X…

Let $G$ be a Lie group with a biinvariant metric, not necessarily positive definite. It is shown that a certain construction carried out in an earlier paper for the fundamental group of a closed surface may be extended to an arbitrary…

It is well known that the Tits boundary of a proper cocompact CAT(0) space embeds into every asymptotic cone of the space. We explore the relationships between the asymptotic cones of a CAT(0) space and its boundary under both the standard…

This paper concerns the self-similarity of topological spaces, in the sense defined in math.DS/0411344. I show how to recognize self-similar spaces, or more precisely, universal solutions of self-similarity systems. Examples include the…

Stiefel manifolds arise naturally as spaces of injective operators and as total spaces of principal bundles over Grassmannians. While their finite-dimensional topology is governed by Bott periodicity, the infinite-dimensional theory…

In this paper, we study the topological rigidity and its relationship with the positivity of scalar curvature. Precisely, we show that any complete contractible $3$-manifold with non-negative scalar curvature is homeomorphic to…

This paper accomplishes two things. First, we construct a geometric analog of the rational Tits building for general noncompact, complete, finite volume $n$-manifolds $M$ of bounded nonpositive curvature. Second, we prove that this analog…

The kth finite subset space of a topological space X is the space exp_k X of non-empty finite subsets of X of size at most k, topologised as a quotient of X^k. The construction is a homotopy functor and may be regarded as a union of…

In this work we introduce a new combinatorial notion of boundary $\Re C$ of an $\omega$-dimensional cubing $C$. $\Re C$ is defined to be the set of almost-equality classes of ultrafilters on the standard system of halfspaces of $C$, endowed…