Related papers: Finite asymptotic dimension for CAT(0) cube comple…

In this paper we continue our earlier investigations into the asymptotic behaviour of infinite systems of coupled differential equations. Under the mild assumption that the so-called characteristic function of our system is completely…

The canonical dimension is an invariant attached to admissible representations of p-adic reductive groups, which has only received significant attention in the case of mod-p representations. In the case of complex representations, the…

We define pure gauge $QCD$ on an infinite strip of width $L$. Techniques similar to those used in finite $TQCD$ allow us to relate $3D$-observables to pure $QCD_2$ behaviors. The non triviality of the $L \arrow 0$ limit is proven and the…

We prove the inequality $$ \as A\ast_CB\le\max\{\as A,\as B,\as C+1\} $$ and we apply this inequality to show that the asymptotic dimension of any right-angled Coxeter group does not exceed the dimension of its Davis' complex.

We study the dimension theory of limit sets of iterated function systems consisting of a countably infinite number of conformal contractions. Our focus is on the Assouad type dimensions, which give information about the local structure of…

We show that the class of CAT(0) spaces is closed under suitable conformal changes. In particular, any CAT(0) space admits a large variety of non-trivial deformations.

We prove that the linearly controlled asymptotic dimension of the fundamental group of any 3-dimensional graph-manifold does not exceed 7. As applications we obtain that the universal cover of such a graph-manifold is an absolute Lipschitz…

We prove that for all $k,m,n \in \mathbb N \cup \{\infty\}$ with $4 \leq k \leq m \leq n$, there exists a finitely generated group $G$ with a finitely generated subgroup $H$ such that the asymptotic dimension of $G$ is $k$, the…

In this paper, we approach the question if some of the separation axioms are equivalent in the class of asymmetric normed spaces. In particular, we make a remark on a known theorem which states that every $T_1$ asymmetric normed space with…

In this short note, we show that a group acting geometrically on a CAT(0) cube complex with virtually abelian hyperplane-stabilisers must decompose virtually as a free product of free abelian groups and surface groups.

In this paper we show that the asymptotic dimension of an unbounded proper metric space is bounded above by a coarse analog of Ponomarev's cofinal dimension of topological spaces, which we call the coarse cofinal dimension. We also show…

Asymptotic property C was introduced by Dranishnikov to study spaces with infinite asymptotic dimension. We show that asymptotic property C is preserved by infinite products. We also show that countable restricted direct products of…

We show that if X is a piecewise Euclidean 2-complex with a cocompact isometry group, then every 2-quasiflat in X is at finite Hausdorff distance from a subset which is locally flat outside a compact set, and asymptotically conical.

We give new examples of hyperbolic and relatively hyperbolic groups of cohomological dimension $d$ for all $d\geq 4$. These examples result from applying CAT$(0)$/CAT$(-1)$ filling constructions (based on singular doubly warped products) to…

We show that the asymptotic boundary conditions of general asymptotically flat black holes in four dimensions can be modified such that a conformal symmetry emerges. The black holes with the asymptotic geometry removed in this manner…

We prove addition and subspace theorems for asymptotic large inductive dimension. We investigate a transfinite extension of this dimension and show that it is trivial.

We study groups acting on CAT(0) square complexes. In particular we show if Y is a nonpositively curved (in the sense of A. D. Alexandrov) finite square complex and the vertex links of Y contain no simple loop consisting of five edges, then…

We study uniform exponential growth of groups acting on CAT(0) cube complexes. We show that groups acting without global fixed points on CAT(0) square complexes either have uniform exponential growth or stabilize a Euclidean subcomplex.…

We characterize the expressive power of quantum circuits with the pseudo-dimension, a measure of complexity for probabilistic concept classes. We prove pseudo-dimension bounds on the output probability distributions of quantum circuits; the…

Let $X$ be a geodesic metric space with $H_1(X)$ uniformly generated. If $X$ has asymptotic dimension one then $X$ is quasi-isometric to an unbounded tree. As a corollary, we show that the asymptotic dimension of the curve graph of a…