Related papers: All subterminal schemes
We stratify families of projective and very affine hypersurfaces according to their topological Euler characteristic. Our new algorithms compute all strata using algebro-geometric techniques. For very affine hypersurfaces, we investigate…
We define the topological complexity sequence of a group as the sequence of topological complexities of its Milnor constructions. This sequence may be regarded as an intrinsic refinement of the topological complexity of a group and, unlike…
We begin the study of completeness of affine connections, especially those on statistical manifolds as well as on affine hypersurfaces. We collect basic facts, prove new theorems and provide examples with remarkable properties.
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part we discus the main structures…
We study automorphisms of the affine line over rings like ZZ/p^n.
The affine group schemes of automorphisms of the multilinear r-fold cross products on finite-dimensional vectors spaces over fields of characteristic not two are determined. Gradings by abelian groups on these structures, that correspond to…
We focus on working on incidence rings, a class of (possibly infinite) matrix rings indexed by ordered sets. Some general properties about them are given, including how they are always the inverse limit of finite matrix rings, giving a…
We construct classifying $\infty$-topoi by showing that the $(\infty,2)$-category of topoi has weighted limits. We show that several prestacks of interest have a classifying topos, including the prestack of spectra.
Topological phases in electronic structures contain a new type of topology, called fragile, which can arise, for example, when an Elementary Band Representation (Atomic Limit Band) splits into a particular set of bands. We obtain, for the…
We describe two types of localization for $(\infty, 1)$-categories which determine the successive terms in the homotopy spectral sequence of a (co)simplicial object.
For a topological space $X$ we study continuous maps $f : X\to \mathbb R^m$ such that images of every pairwise distinct $k$ points are affinely (linearly) independent. Such maps are called affinely (linearly) $k$-regular embeddings. We…
A notion of heaps of modules as an affine version of modules over a ring or, more generally, over a truss, is introduced and studied. Basic properties of heaps of modules are derived. Examples arising from geometry (connections, affine…
We study Michael's lower semifinite topology and Fell's topology on the collection of all closed limit subsets of a topological space. Special attention is given to the subfamily of all maximal limit sets.
We show that any of a large class of schemes receives a universal homeomorphism from a reduced scheme that in turn receives no nontrivial universal homeomorphism from any other reduced scheme. This construction serves as a categorical input…
The purpose of this note is to start the systematic analysis of cofinal types of topological groups.
The note focuses on the differential geometric approach to the study of nonlinear systems that are affine in control. We first develop normal forms for nonlinear system affine in control. Based on these normal forms, we then address the…
In this paper, we describe some recent results obtained in the context of vector subdivision schemes which possess the so-called full rank property. Such kind of schemes, in particular those which have an interpolatory nature, are connected…
We consider embeddings of a finite complex in a sphere. We give a homotopy theoretic classification of such embeddings in a wide range.
We recall and delve into the different characterizations of the depth of an affine semigroup ring, providing an original characterization of depth two in three and four dimensional cases which are closely related to the existence of a…
A quandle will be called quasi-affine, if it embeds into an affine quandle. Our main result is a characterization of quasi-affine quandles, by group-theoretic properties of their displacement group, by a universal algebraic condition coming…