Related papers: Cubulating spaces with walls
An important conjecture within the AdS/CFT correspondence relates holographic spacetime to the quantum computational complexity of the dual quantum field theory. However, the quantitative understanding of this relation is still an open…
Recall that the moduli space of smooth (that is, stable) cubic curves is isomorphic to the quotient of the upper half plane by the group of fractional linear transformations with integer coefficients. We establish a similar result for…
Modularity is a promising approach for scaling up quantum computers and therefore integrating higher qubit counts. The essence of such architectures lies in their reliance on high-fidelity and fast quantum state transfers enabled by…
There exist cubical transition systems containing cubes having an arbitrarily large number of faces. A regular transition system is a cubical transition system such that each cube has the good number of faces. The categorical and…
We define Cayley structures as a field of Cayley's ruled cubic surfaces over a four dimensional manifold and motivate their study by showing their similarity to indefinite conformal structures and their link to differential equations. In…
In this article we give an explicit algorithm which will determine, in a discrete and computable way, whether a finite piecewise Euclidean complex is non-positively curved. In particular, given such a complex we show how to define a boolean…
We study the scalar curvature of incomplete wedge metrics in certain stratified spaces with a single singular stratum (wedge spaces). Building upon several well established technical tools for this category of spaces (the corresponding…
We establish several inequalities for manifolds with positive scalar curvature and, more generally, for the scalar curvature bounded from below, in the spirit of the classical bound on the distances between conjugates points in surfaces…
We discuss domain walls from spontaneous breaking of Abelian discrete symmetries $Z_N$. A series of different domain wall structures are predicted, depending on the symmetry and charge assignments of scalars leading to the spontaneous…
We show that groups satisfying Kazhdan's property (T) have no unbounded actions on finite dimensional CAT(0) cube complexes, and deduce that there is a locally CAT(-1) Riemannian manifold which is not homotopy equivalent to any finite…
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…
We consider a geometrization, i.e., we identify geometrical structures, for the space of density states of a quantum system. We also provide few comments on a possible application of this geometrization for composite systems.
We investigate domain-wall/quantum field theory correspondences in various dimensions. Our general analysis does not only cover the well-studied cases in ten and eleven dimensions but also enables us to discuss new cases like a Type…
The article contains a brief description on the study of conformal scalar curvature equations, and discusses selected topics and questions concerning the equations in open spaces.
We consider a model with a real scalar field with polynomial self-interaction of the fourth degree and a coupled scalar triplet. We demonstrate that there is an exact analytic solution in the form of a domain wall with a localised…
We investigate vortices on a cylinder in supersymmetric non-Abelian gauge theory with hypermultiplets in the fundamental representation. We identify moduli space of periodic vortices and find that a pair of wall-like objects appears as the…
We study complexes of stable $\infty$-categories, referred to as categorical complexes. As we demonstrate, examples of such complexes arise in a variety of subjects including representation theory, algebraic geometry, symplectic geometry,…
We consider asymptotic dimension of coarse spaces. We analyse coarse structures induced by metrisable compactifications. We calculate asymptotic dimension of coarse cell complexes. We calculate the asymptotic dimension of certain negatively…
We describe the canonical correspondence between set of all finite metric spaces and set of special symmetric convex polytopes, and formulate the problem about classification of the metric spaces in terms of combinatorial structure of those…
In this paper we start the inquiry into proving uniform exponential growth in the context of groups acting on CAT(0) cube complexes. We address free group actions on CAT(0) square complexes and prove a more general statement. This says that…