Related papers: Higher order Nielsen numbers

We study the polynomial approximation of symmetric multivariate functions and of multi-set functions. Specifically, we consider $f(x_1, \dots, x_N)$, where $x_i \in \mathbb{R}^d$, and $f$ is invariant under permutations of its $N$…

Vladimir Shpilrain and Jie-Tai Yu have asked for an effective algorithm to decide if two elements of C[x,y] are related by an automorphism of C[x,y]. We describe here an efficient algorithm that decides this question and finds the…

In this article, we offer group-theoretic, field-theoretic, and topological interpretations of the Gaussian binomial coefficients and their sum. For a finite $p$-group $G$ of rank $n$, we show that the Gaussian binomial coefficient…

With a view toward a fracton theory in condensed matter, we introduce a higher-moment polynomial degree-p global symmetry, acting on complex scalar/vector/tensor fields (e.g., ordinary or vector global symmetry for p$=0$ and p$=1$…

Many applications modeled by polynomial systems have positive dimensional solution components (e.g., the path synthesis problems for four-bar mechanisms) that are challenging to compute numerically by homotopy continuation methods. A…

Let $\mathcal{N} \subset \mathbb{R}^M$ be a smooth simply connected compact manifold without boundary. A rational homotopy subgroup of $\pi_{N}(\mathcal{N})$ is represented by a homomorphism \[{\rm deg}: \pi_{N}(\mathcal{N}) \to…

Given a connected manifold with corners of any codimension there is a very basic and computable homology theory called conormal homology defined in terms of faces and orientations of their conormal bundles, and whose cycles correspond…

Let $X = G/\Gamma$, where $G$ is a Lie group and $\Gamma$ is a lattice in $G$, and let $U$ be a subset of $X$ whose complement is compact. We use the exponential mixing results for diagonalizable flows on $X$ to give upper estimates for the…

The aim of this paper is to generalize some of the properties and results regarding both the coincidence point set and the common fixed point set of any two digitally continuous maps to the case of several (more than two) digitally…

In this paper we study 2-valued non-split maps, focusing on the Klein bottle. We establish a connection between a 2-valued non-split map $\phi:X\multimap Y$ and a pair of classes of maps $([f],[f\circ \delta])\in [\tilde X,Y]\times[\tilde…

Let $f\colon (\mathbb C^n,S)\to (\mathbb C^p,0)$ be a finite map-germ with $n<p$ and $Y_\delta$ the image of a small perturbation $f_\delta$. We show that the reduced cohomology of $Y_\delta$ is concentrated in a range of degrees determined…

We investigate the intersection problem for finite semigroups, which asks for a given set of regular languages, represented by recognizing morphisms to finite semigroups, whether there exists a word contained in their intersection. We…

The coincidence problem for planar patterns with $N$-fold symmetry is considered. For the N-fold symmetric module with $N<46$, all isometries of the plane are classified that result in coincidences of finite index. This is done by…

The aim of this article is to explain a philosophy for applying higher dimensional Seifert-van Kampen Theorems, and how the use of groupoids and strict higher groupoids resolves some foundational anomalies in algebraic topology at the…

In this article we study the bordism groups of normally nonsingular maps $f: X \to Y$ defined on pseudomanifolds $X$ and $Y$. To characterize the bordism of such maps, inspired by the formula given by Stong, we give a general definition of…

We present an algorithm that, given finite simplicial sets $X$, $A$, $Y$ with an action of a finite group $G$, computes the set $[X,Y]^A_G$ of homotopy classes of equivariant maps $\ell \colon X \to Y$ extending a given equivariant map $f…

Lie group theory states that knowledge of a $m$-parameters solvable group of symmetries of a system of ordinary differential equations allows to reduce by $m$ the number of equation. We apply this principle by finding dilatations and…

We introduce a directed graph related to a group $G$, which we call the N-prime graph $\Gamma_{\rm{N}}(G)$ of $G$ and which is a refinement of the classical Gruenberg-Kegel graph. The vertices of $\Gamma_{\rm{N}}(G)$ are the primes $p$ such…

Suppose G is a connected, simple, real Lie group with real rank at least two, M is an ergodic G-space with invariant probability measure, and f is a Homeo(T)-valued Borel cocycle, where Homeo(T) denotes the group of homeomorphisms of the…

We study graph complexes related to configuration spaces and diffeomorphism groups of highly connected manifolds of odd dimension. In particular we compute the cohomology in the "high genus" limit. This paper is a continuation of previous…