Related papers: Local Matrix Homotopies and Soft Tori

In this document we study the local connectivity of the sets whose elements are $m$-tuples of pairwise commuting normal matrix contractions. Given $\varepsilon>0$, we prove that there is $\delta>0$ such that for any two $m$-tuples of…

In this document we study the local path connectivity of sets of $m$-tuples of commuting normal matrices with some additional geometric constraints in their joint spectra. In particular, given $\varepsilon>0$ and any fixed but arbitrary…

In this document we study the uniform local path connectivity of sets of $m$-tuples of pairwise commuting normal matrices with some additional constraints. More specifically, given given $\varepsilon>0$, a fixed metric $\eth$ in…

It is well known that many local graph problems, like Vertex Cover and Dominating Set, can be solved in 2^{O(tw)}|V|^{O(1)} time for graphs G=(V,E) with a given tree decomposition of width tw. However, for nonlocal problems, like the…

In this document we study some local deformation properties of matrix representations of the universal C$^*$-algebras denoted by $\mathbb{I}^{m}_\varepsilon[p_1,\ldots,p_m]$ and $\mathbb{S}^{m-1}_\varepsilon[p_1,\ldots,p_m]$, and that we…

We prove a rigidity property for mapping tori associated to minimal topological dynamical systems using tools from noncommutative geometry. More precisely, we show that under mild geometric assumptions, an orientation-preserving leafwise…

For any $n\geq k\geq l\in\mathbb{N},$ let $S(n,k,l)$ be the set of all those non-negative definite matrices $a\in M_{n}(\mathbb{C})$ with $l\leq\text{rank }a\leq k$. Motivated by applications to $C^{*}$-algebra theory, we investigate the…

A linear connection on a Lie algebroid is called a Cartan connection if it is suitably compatible with the Lie algebroid structure. Here we show that a smooth connected manifold $M$ is locally homogeneous - i.e., admits an atlas of charts…

Torus networks of moderate degree have been widely used in the supercomputer industry. Tori are superb when used for executing applications that require near-neighbor communications. Nevertheless, they are not so good when dealing with…

Let $X$ be a locally 1-connected metric space and $A_1,A_2,...,A_n$ be connected, locally path connected and compact pairwise disjoint subspaces of $X$. In this paper, we show that the quotient space $X/(A_1,A_2,...,A_n)$ obtained from $X$…

In this study, the soft usual topology compatible with the usual topology of $\mathbb{R}$ is defined, and using its subspace topology on the interval $[0,1]$, the concept of a soft path is introduced. Within this context, the notions of…

We present the local classification of singularities of smooth vector fields on the line, with respect to the equivalence relation of $C^1$--conjugacy. Along the way, we recall the analogous classification, up to $C^0$ and $C^{\infty}$…

This paper considers the recovery of a rank $r$ positive semidefinite matrix $X X^T\in\mathbb{R}^{n\times n}$ from $m$ scalar measurements of the form $y_i := a_i^T X X^T a_i$ (i.e., quadratic measurements of $X$). Such problems arise in a…

We discuss the homotopy type and the cohomology of spaces of locally convex parametrized curves gamma: [0,1] -> S^2, i.e., curves with positive geodesic curvature. The space of all such curves with gamma(0) = gamma(1) = e_1 and gamma'(0) =…

Motivated by the definition of the smooth manifold structure on a suitable mapping space, we consider the general problem of how to transfer local properties from a smooth space to an associated mapping space. This leads to the notion of…

We present a new topological connection method for the local bilinear computation of Jacobi sets that improves the visual representation while preserving the topological structure and geometric configuration. To this end, the topological…

By a tensor we mean an element of a tensor product of vector spaces over a field. Up to a choice of bases in factors of tensor products, every tensor may be coordinatized, that is, represented as an array consisting of numbers. This note is…

In this paper we address the classification problem for locally compact (n-1)-connected CW-complexes with dimension less or equal than n+2 up to proper homotopy type. We obtain complete classification theorems in terms of purely algebraic…

We show that if the image of a Legendrian submanifold under a contact homeomorphism (i.e. a homeomorphism that is a $C^0$-limit of contactomorphisms) is smooth then it is Legendrian, assuming only positive local lower bounds on the…

Let $M, N$ the be smooth manifolds, $\mathcal{C}^{r}(M,N)$ the space of ${C}^{r}$ maps endowed with weak $C^{r}$ Whitney topology, and $\mathcal{B} \subset \mathcal{C}^{r}(M,N)$ an open subset. It is proved that for $0\leq r<s\leq\infty$…