Related papers: Multiplicity of continuous maps between manifolds

Given a set $X\subseteq\mathbb{R}^2$ of $n$ points and a distance $d>0$, the multiplicity of $d$ is the number of times the distance $d$ appears between points in $X$. Let $a_1(X) \geq a_2(X) \geq \cdots \geq a_m(X)$ denote the…

Let $f:M^m\to N^n$ be a smooth map between two differential manifolds with $N$ connected, $f(M)$ closed and $f(M)\neq N$. In this short note, we show that either all the points of $M$ are critical points of $f$ or the dimension the…

We consider the inclusion of the space of algebraic (regular) maps between real algebraic varieties in the space of all continuous maps. For a certain class of real algebraic varieties, which include real projective spaces, it is well known…

This paper is devoted to studying of some properties of multivalued mappings in Euclidean space. There were proved theorems on a fixed point for multivalued mappings whose restrictions to some subset in the closure of a domain satisfy "a…

In this note, we give a brief exposition on the differences and similarities between strictly nef and ample vector bundles, with particular focus on the circle of problems surrounding the geometry of projective manifolds with strictly nef…

We provide a partial answer to the following problem: \emph{give an effective upper bound on the multiplicity of non-isolated common zero of a tuple of Noetherian functions}. More precisely, consider a foliation defined by two commuting…

We consider a class $\mathcal{F}$ of Markov multi-maps on the unit interval. Any multi-map gives rise to a space of trajectories, which is a closed, shift-invariant subset of $[0,1]^{\mathbb{Z}_+}$. For a multi-map in $\mathcal{F}$, we show…

In this paper we investigate Abel maps on normal surface singularities described in \cite{NNI}. We investigate the affine version of the class of the images of Abel maps on normal surface singularities. More precisely we consider the…

Characterized are all simple undirected graphs $G$ such that any real symmetric matrix that has graph $G$ has no eigenvalues of multiplicity more than 2. All such graphs are partial 2-trees (and this follows from a result for rather general…

For a closed Riemannian manifold $M$ with a compact Lie group $G$ acting by isometries, we show a generic multiplicity one theorem in equivariant min-max theory, and show in generic sense that there are infinitely many $G$-invariant minimal…

Let M be a manifold endowed with a symmetric affine connection $\Gamma.$ The aim of this paper is to describe a quantization map between the space of second-order polynomials on the cotangent bundle T^{*} M and the space of second-order…

We work within the framework of a program aimed at exploring various extended versions for theorems from a class containing Borsuk-Ulam type theorems, some fixed point theorems, the KKM lemma, Radon, Tverberg, and Helly theorems. In this…

Let $f_1,...,f_k:M\to N$ be maps between closed manifolds, $N(f_1,...,f_k)$ and $R(f_1,...,f_k)$ be the Nielsen and the Reideimeister coincidence numbers respectively. In this note, we relate $R(f_1,...,f_k)$ with…

We study the space of link maps, which are smooth maps from the disjoint union of manifolds P and Q to a manifold N such that the images of P and Q are disjoint. We give a range of dimensions, interpreted as the connectivity of a certain…

For a graph G, M(G) denotes the maximum multiplicity occurring of an eigenvalue of a symmetric matrix whose zero-nonzero pattern is given by edges of G. We introduce two combinatorial graph parameters T^-(G) and T^+(G) that give a lower and…

Let X be a compact (resp. compact and nonsingular) real algebraic variety and let Y be a homogeneous space for some linear real algebraic group. We prove that a continuous (resp. C^infinity) map f:X-->Y can be approximated by regular maps…

A vector field E on an F-manifold (M, o, e) is an eventual identity if it is invertible and the multiplication X*Y := X o Y o E^{-1} defines a new F-manifold structure on M. We give a characterization of such eventual identities, this being…

In \cite{NNM} the author with A. N\'emethi computed the multiplicity of generic surface singularities, the formula is purely topological computable from the resolution graph of the surface singularity. In the present paper we extend the…

We develop a new purely combinatorial approach to N. Steenrod's problem on realisation of cycles. We prove that every n-dimensional homology class of every topological space can be realised with some multiplicity by an image of a…

In this note we make use of some properties of vector fields on a manifold to give an alternate proof to [3] for the equivalence between connections and parallel transport on vector bundles over manifolds. Out of the proof will emerge a new…