Related papers: Singular points in generic two-parameter families …
We analyze several issues concerning the singular vectors of the Topological N=2 Superconformal algebra. First we investigate which types of singular vectors exist, regarding the relative U(1) charge and the BRST-invariance properties,…
Special-generic-like maps or SGL maps are introduced by the author motivated by observing and investigating algebraic topological or differential topological properties of manifolds via nice smooth maps whose codimensions are negative. The…
We describe some families of differentiable vector fields with the Hopf bifurcation at infinity, without assuming the continuous differentiability. These vector fields have isolated singular points on the plane, and the initial families are…
We introduce the notion of a bisector field, which is a maximal collection of pairs of lines such that for each line in each pair, the midpoint of the points where the line crosses every pair is the same, regardless of choice of pair. We…
We describe all possible structures of discrete vector field (discrete Morse functions) with minimal number of critical cells on the regular CW-complex for the 2-disk (1 cell), the 2-sphere (2 cells), the cylinder (2 cells) and Mobius band…
Parameter-dependent quantum systems often exhibit energy degeneracy points, whose comprehensive description naturally lead to the application of methods from singularity theory. A prime example is an electronic band structure where two…
A set of unit vectors in $\mathbb{R}^d$ is a called a spherical two-distance set if the inner products of distinct vectors only take two values. In this paper, we give explicit correspondence between spherical two-distance sets and graphs…
We construct some examples of polynomial maps over finite fields that admit subvarieties with a peculiar property: every geometric point is mapped to a fixed point by some iteration of the map, while the whole subvariety is not. Several…
A 2-web in the plane is given by two everywhere transverse 1-foliations. In this paper we introduce the study of singular 2-webs, given by any two foliations, which may be tangent in some points. We show that such two foliations are tangent…
We generalize Khintchine's method of constructing totally irrational singular vectors and linear forms. The main result of the paper shows existence of totally irrational vectors and linear forms with large uniform Diophantine exponents on…
The genus spectrum of a finite group $G$ is the set of all $g\geq 2$ such that $G$ acts faithfully and orientation-preserving on a closed compact orientable surface of genus $g$. This article is an overview of some results relating the…
Let $G$ be a strictly pseudoconvex domain in $\mathbb{C}^2$ with $C^\infty$-smooth boundary $\partial G$. Let $S$ be a 2-dimensional sphere embedded into $\partial G$. Denote by $\mathcal{E}$ the set of all complex points on $S$. We study…
We introduce the concept of the touching of two multifunctions on a real Hilbert space, and deduce that certain multifunctions on the space have a unique fixed point. These result are applied to the theory of genaralized cycles and…
Special generic maps are higher dimensional versions of Morse functions with exactly two singular points, characterizing spheres topologically except $4$-dimensional cases: in these cases standard spheres are characterized. Canonical…
In this article we discuss local aspects of 2-functors defined on the path 2-groupoid of a smooth manifold; in particular, local trivializations and descent data. This is a contribution to a project that provides an axiomatic formulation of…
We study how to construct explicit deformations of generic smooth maps from closed $n$--dimensional manifolds $M$ with $n \geq 2$ to the $2$--sphere $S^2$ and show that every smooth map $M \to S^2$ is homotopic to a $C^\infty$ stable map…
Special generic maps are higher dimensional versions of Morse functions with exactly two singular points, characterizing spheres topologically except 4-dimensional cases and 4-dimensional standard spheres. The class of such maps also…
We consider the Lie algebra of all vector fields on a contact manifold as a module over the Lie subalgebra of contact vector fields. This module is split into a direct sum of two submodules: the contact algebra itself and the space of…
Landmark manifolds consist of a collection of distinct points, and dynamics on this manifold can be used to represent flows, such as solutions of ODEs and flows deforming a shape. We will consider landmark configurations in the Euclidean…
We investigate families of two-dimensional simplicial complexes defined in terms of vertex decompositions. They include nonevasive complexes, strongly collapsible complexes of Barmak and Miniam and analogues of 2-trees of Harary and Palmer.…