Related papers: Classification of digital n-manifolds

We classify homogeneous pseudo-Riemannian manifolds of index 4 which admit an invariant almost hyper-Hermitian structure and an H-irreducible isotropy group. The main result is that all these spaces are flat except in dimension 12.

Let N and P be smooth manifolds of dimensions n and p (n>=p>=2). Let Omega^{I}(N,P) denote an open subspace of J(N,P) which consists of all Boardman submanifolds Sigma^{J}(N,P) with J=< I in the lexicographic order. We will prove the…

This paper presents a classification of the total spaces of $S^3$-bundles over $\mathbb{C}P^2$ up to orientation-preserving homotopy equivalence. Our approach proceeds in two steps: we first derive the PL-homeomorphism classification for…

We define an invariant, which we call surface-complexity, of closed 3-manifolds by means of Dehn surfaces. The surface-complexity of a manifold is a natural number measuring how much the manifold is complicated. We prove that it fulfils…

Given an $n$-gon, the poset of all collections of pairwise non-crossing diagonals is isomorphic to the face poset of some convex polytope called \textit{associahedron}. We replace in this setting the $n$-gon (viewed as a disc with $n$…

The class of the hypercomplex pseudo-Hermitian manifolds is considered. The flatness of the considered manifolds with the 3 parallel complex structures is proved. Conformal transformations of the metrics are introduced. The conformal…

In this paper, we examine the relations of two closely related concepts, the digital Lusternik-Schnirelmann category and the digital higher topological complexity, with each other in digital images. For some certain digital images, we…

In this paper we investigate properties of digital spaces which are represented by graphs. We find conditions for digital spaces to be digital n-manifolds and n-spheres. We study properties of partitions of digital spaces and prove a…

A p-compact group is a mod p homotopy theoretical analogue of a compact Lie group. It is determined the homotopy nilpotency class of a p-compact group having the homotopy type of the $p$-completion of the direct product of spheres.

We classify $n$-dimensional geometric graph manifolds with nonnegative scalar curvature, and first show that if $n>3$, the universal cover splits off a codimension 3 Euclidean factor. We then proceed with the classification of the…

In this note, we provide a unifying framework to investigate the computational complexity of classical spin models and give the full classification on spin models in terms of system dimensions, randomness, external magnetic fields and types…

This is an exposition of results on the existence problem of $\pi_1$-injective immersed and embedded surfaces in graph-manifolds, and also of nonpositively curved metrics on graph-manifolds, obtained by different authors. The results are…

We calculate the rational cohomology of the classifying space of the diffeomorphism group of the manifolds $U_{g,1}^n:= \#^g(S^n \times S^{n+1})\setminus \mathrm{int}{D^{2n+1}}$, for large $g$ and $n$, up to approximately degree $n$. The…

In this paper we study the homotopy type of $\Hom(C_m,C_n)$, where $C_k$ is the cyclic graph with $k$ vertices. We enumerate connected components of $\Hom(C_m,C_n)$ and show that each such component is either homeomorphic to a point or…

We determine those smooth $n$--dimensional closed manifolds with $n \geq 4$ which admit round fold maps into ${\mathbb{R}}^{n-1}$, i.e.\ fold maps whose critical value sets consist of disjoint spheres of dimension $n-2$ isotopic to…

A common observation in data-driven applications is that high-dimensional data have a low intrinsic dimension, at least locally. In this work, we consider the problem of point estimation for manifold-valued data. Namely, given a finite set…

Given a smooth map $f:M\rightarrow N$ of closed oriented smooth manifolds, is there an immersion homotopic to $f$? We provide an algorithm that decides this when the codimension of the manifolds is odd.

A procedure for the construction and the classification of multilattices in arbitrary dimension is proposed. The algorithm allows to determine explicitly the location of the points of a multilattice given its space group, and to determine…

In this paper we survey $n$-dimensional solenoidal manifolds for $n=1,2$ and 3, and present new results about them. Solenoidal manifolds of dimension $n$ are metric spaces locally modeled on the product of a Cantor set and an open…

For an element $\Psi$ in the graded vector space $\Omega^*(M, TM)$ of tangent bundle valued forms on a smooth manifold $M$, a $\Psi$-submanifold is defined as a submanifold $N$ of $M$ such that $\Psi_{|N} \in \Omega^*(N, TN)$. The class of…