Related papers: Cubulating spaces with walls

Weak topologies that yield weak convergence for bounded sequences and nets in CAT($0$) spaces have been studied in the past. We are here concerned with weak topologies that yield weak convergence of unbounded sequences and nets. We analyze…

We consider actions of locally compact groups $G$ on certain CAT(0) spaces $X$ by isometries. The CAT(0) spaces we consider have finite dimension at large scale. In case $B$ is a $G$-boundary, that is a measurable $G$-space with amenability…

There are versions of "calculus" in many settings, with various mixtures of algebra and analysis. In these informal notes we consider a few examples that suggest a lot of interesting questions.

In this project we explore the geometry of general metric spaces, where we do not necessarily have the tools of differential geometry on our side. Some metric spaces $(X,d)$ allow us to define geodesics, permitting us to compare geodesic…

We study the acylindrical hyperbolicity of groups acting by isometries on CAT(0) cube complexes, and obtain simple criteria formulated in terms of stabilisers for the action. Namely, we show that a group acting essentially and…

We find a one-to-one correspondence between full extrinsic symmetric spaces in (possibly degenerate) inner product spaces and certain algebraic objects called (weak) extrinsic symmetric triples. In particular, this yields a description of…

We present a new approach to scalable quantum computing--a ``qubus computer''--which realises qubit measurement and quantum gates through interacting qubits with a quantum communication bus mode. The qubits could be ``static'' matter qubits…

We provide a necessary and sufficient condition on a finite flag simplicial complex, L, for which there exists a unique CAT(0) cube complex whose vertex links are all isomorphic to L. We then find new examples of such CAT(0) cube complexes…

If G is a group acting properly by semisimple isometries on a proper CAT(0) space X, then we build models for the classifying spaces E_{vc} and E_{fbc} under the additional assumption that the action of G has a well-behaved collection of…

We show that the sublinear Morse boundary of every CAT(0) space continuously injects into the Gromov boundary of a hyperbolic space, which was not previously known even for all CAT(0) cube complexes. Our work utilizes the curtain machinery…

The conformal compactification is considered in a hierarchy of hypercomplex projective spaces with relevance in physics including Minkowski and Anti-de Sitter space. The geometries are expressed in terms of bicomplex Vahlen matrices and…

Computability theory is used to evaluate the complexity of classifying various kinds of Lebesgue spaces and associated isometric isomorphism problems.

The conformal geometry of surfaces in the conformal space $\mathbf Q^n_1$ is studied. We classify the space-like surfaces in $\mathbf Q^n_1$ with vanishing conformal form up to conformal equivalence.

We extend the correspondence between adS-supergravities and superconformal field theories on the adS boundary to a correspondence between gauged supergravities (typically with non-compact gauge groups) and quantum field theories on domain…

The correspondence between quantum mechanics and noncommutative geometry is illustrated in the context of the noncommutative ${\rm AdS}^2_{\theta}/{\rm CFT_1}$ duality where ${\rm CFT}_1$ is identified as conformal quantum mechanics. This…

We study multihomogeneous spaces corresponding to ${\mathbb Z}^n$-graded algebras over an algebraically closed field of characteristic 0 and their relation with the description of $T$-varieties.

We initiate the study of correspondences for Smale spaces. Correspondences are shown to provide a notion of a generalized morphism between Smale spaces and are a special case of finite equivalences. Furthermore, for shifts of finite type, a…

We study asymptotic topological regularity of CAT(0) spaces. We prove that if a purely n-dimensional, proper, geodesically complete CAT(0) space has small volume growth, then it is homeomorphic to the n-dimensional Euclidean space. We also…

Cubical rectangles are being defined and explored here over the $n-$dimensional geometric cube $Q_n.$ They form a new class of geometric objects that includes all the edges and all the squares of the $n-$cube. We enumerate and characterize…

For metric spaces with curvature less than or equal to x, x<0, it is shown that a recurrent geodesic can be approximated by closed geodesics. A counter example is provided for the converse.