Related papers: On 2-dimensional nonaspherical cell-like Peano con…
We prove a structural result for geometrically non-reduced varieties and give applications to Fano varieties. For example, we show that if $X$ is the generic fibre of a Mori fibre space of relative dimension $n$, and the characteristic is…
We consider the moduli space of flat G-bundles over the twodimensional torus, where G is a real, compact, simple Lie group which is not simply connected. We show that the connected components that describe topologically non-trivial bundles…
For a differential form on a manifold, having constant components in suitable local coordinates trivially implies being parallel relative to a torsion-free connection, and the converse implication is known to be true for $p$-forms in…
We classify the irreducible components of the space of foliations on Fano 3-folds with rank one Picard group. As a corollary we obtain a classification of holomorphic Poisson structures on the same class of 3-folds.
An $A$-cellular space is a space built from $A$ and its suspensions, analogously to the way that $CW$-complexes are built from $S^0$ and its suspensions. The $A$-cellular approximation of a space $X$ is an $A$-cellular space $CW_{A}X$ which…
We prove that the deformations of a smooth complex Fano threefold X with Picard number 1, index 1, and degree 10, are unobstructed. The differential of the period map has two-dimensional kernel. We construct two two-dimensional components…
To a closed connected oriented surface $S$ of genus $g$ and a nonempty finite subset $P$ of $S$ is associated a simplicial complex (the arc complex) that plays a basic r\^ ole in understanding the mapping class group of the pair $(S,P)$. It…
Defining cellular sheaves beyond graph structures, such as on simplicial complexes containing higher-dimensional simplices, is an essential and intriguing topic in topological data analysis (TDA) and the development of sheaf neural…
A non-trivial separable metric space $X$ is called an almost homology $n$-manifold if the homology groups $H_k(X,X\backslash\{x\},\mathbb Z)$ are trivial for all $x\in X$ and all $k=0,1,..,n-1$. We provide a necessary and sufficient…
An alternative foundation for 2-categories is explored by studying graph-theoretically a partial operation on 2-cells named juncture, which can replace vertical and horizontal composition. Juncture is a generalized vertical composition of…
Topological dynamics of cellular automata (CA), inherited from classical dynamical systems theory, has been essentially studied in dimension 1. This paper focuses on higher dimensional CA and aims at showing that the situation is different…
We develop a general theory for irreducible homogeneous spaces $M= G/H$, in relation to the nullity $\nu$ of their curvature tensor. We construct natural invariant (different and increasing) distributions associated with the nullity, that…
A class of Cantor-type spaces and related geometric structures are discussed.
Peano partial cubes are the bipartite graphs whose geodesic interval spaces are (closed) join spaces. They are the partial cubes all of whose finite convex subgraphs have a pre-hull number which is at most 1. Special Peano partial cubes are…
In this paper, we address the construction of homotopy bicategories of $(\infty,2)$-categories, which we take as being modeled by 2-fold Segal spaces. Our main result is the concrete construction of a functor $h_2$ from the category of…
Column-convex polyominoes are by now a well-explored model. So far, however, no attention has been given to polyominoes whose columns can have either one or two connected components. This little known kind of polyominoes seems not to be…
We show that if $X$ is an arc-like continuum, then for every point $x \in X$ there is a plane embedding of $X$ in which $x$ is an accessible point. This answers a question posed by Nadler in 1972, which has become known as the Nadler-Quinn…
Most of the non-Abelian string-vortices studied so far are characterized by two-dimensional \cpn models with various degrees of supersymmetry on their world sheet. We generalize this construction to "composite" non-Abelian strings…
In this work are considered some questions of Monte-Carlo modeling on nontrivial bundles. As a basic example is used problem of generation of straight lines in 3D space, related with modeling of interaction of a solid body with a flux of…
A continuum is hereditarily equivalent if it is homeomorphic to each of its non-degenerate sub-continua. We show in this paper that the arc and the pseudo-arc are the only non-degenerate hereditarily equivalent plane continua.