Related papers: General theory of lifting spaces

We construct a one dimensional, second countable, simply connected manifold that exhibits a single non Hausdorff fiber, sufficient to destroy the fundamental properties of classical covering space theory. The space, called the line with k…

We prove sandwich theorems and a Tauberian theorem in the space of compact metric measure spaces, endowed with the Gromov-Hausdorff-Prokhorov (GHP) topology. These results hold with respect to a close relative of Gromov's Lipschitz order.…

We prove that the upper blow-up theorem in the Engel group holds for $C^1$ submanifolds. Combining this result with the known negligibility of the singular set, we obtain an integral representation of the spherical measure for all surfaces…

In this paper, we study the geometry of surfaces with the generalised simple lift property. This work generalises previous results by Bernstein and Tinaglia, and it is motivated by the fact that leaves of a minimal lamination obtained as a…

In the theory of crossed modules, considering arbitrary self-actions instead of conjugation allows for the extension of the concept of crossed modules and thus the notion of generalized crossed module emerges. In this paper we give a…

We prove existence of extension dimension for paracompact spaces. Here is the main result of the paper: \proclaim{Theorem} Suppose X is a paracompact space. There is a CW complex K such that {a.} K is an absolute extensor of X up to…

We prove a conjecture of Griffiths on simultaneous normalization of all periods which asserts that the image of the lifted period map on the universal cover lies in a bounded domain in a complex Euclidean space. As an application we prove…

The notions of compactness and Hausdorff separation for generalized enriched categories allow us, as classically done for the category $\mathsf{Top}$ of topological spaces and continuous functions, to study $\textit{compactly generated…

This study focuses on defining normal and strictly convex structures within Menger cone PM-space. It also presents a shared fixed point theorem for the existence of two self-mappings constructed on a strictly convex probabilistic cone…

This paper forms the second part of a series by the authors [GMV1,GMV3] concerning the structure theory of nilspaces of Antol\'in Camarena and Szegedy. A nilspace is a compact space $X$ together with closed collections of cubes…

Let $\mathcal{N}$ be a smooth, compact, connected Riemannian manifold without boundary. Let $\mathcal{E}\to\mathcal{N}$ be the Riemannian universal covering of $\mathcal{N}$. For any bounded, smooth domain $\Omega\subseteq\mathbb{R}^d$ and…

We introduce the theory of generalised ultracategories, these are relational extensions to ultracategories as defined by Lurie. An essential example of generalised ultracategories are topological spaces, and these play a fundamental role in…

We develop dimension theory for a large class of structures called espaliers, consisting of a set $L$ equipped with a partial order $\leq$, an orthogonality relation $\perp$, and an equivalence relation $\sim$, subject to certain axioms.…

In this paper, using the remarkable orthonormal wavelet basis constructed recently by Auscher and Hyt\"onen, we establish the theory of product Hardy spaces on spaces ${\widetilde X} = X_1\times X_2\times\cdot \cdot\cdot\times X_n$, where…

We give a proof of a Conjecture of Walker which states that one can recover the lengths of the bars of a circular linkage from the cohomology ring of the configuration space. For a large class of length vectors, this has been shown by…

For a large class of metric spaces with nice local structure, which includes Banach-Finsler manifolds and geodesic spaces of curvature bounded above, we give sufficient conditions for a local homeomorphism to be a covering projection. We…

The Reeb space of a smooth map whose codimension is minus is the space defined as the space of all connected components of inverse images. For generic maps such as Morse functions and their higher dimensional versions, they are polyhedra…

Using the theory of group action, we first introduce the concept of the automorphism group of an exponential family or a graphical model, thus formalizing the general notion of symmetry of a probabilistic model. This automorphism group…

Let $X$ be an integral projective variety of codimension two, degree $d$ and dimension $r$ and $Y$ be its general hyperplane section. The problem of lifting generators of minimal degree $\sigma$ from the homogeneous ideal of $Y$ to the…

G\"ahler ([4],[5]) introduced and investigated the notion of 2-metric spaces and 2-normed spaces in sixties. These concepts are inspired by the notion of area in two dimensional Euclidean space. In this paper, we choose a fundamentally…