Zobrazeno 1 - 10
of 45
pro vyhledávání: '"Zapata, Cesar A Ipanaque"'
We present the notion of complexity $\text{C}(G,H)$ of two graphs $G$ and $H$, along with basic results for this numerical invariant. This was motivated by the Data Migration Problem. This invariant $\text{C}(G,H)$ is a number that measures \aspas{co
Externí odkaz:
http://arxiv.org/abs/2411.16547
Autor:
Zapata, Cesar A. Ipanaque
The genus of a fibration was introduced by Schwarz in 1962. Given a continuous map $g:A\to B$, the usual sectional number $\text{sec}_u(g)$ is the least integer~$m$ such that $B$ can be covered by $m$ open subsets, each of which admits a local sectio
Externí odkaz:
http://arxiv.org/abs/2410.22515
For a Hausdorff space $Y$, a topological space $X$ and a map $g:X\to Y$, we present a connection between the relative sectional number of the first coordinate projection $\pi_{2,1}^Y:F(Y,2)\to Y$ with respect to $g$, and the coincidence property (CP)
Externí odkaz:
http://arxiv.org/abs/2408.07316
We present the notion of injective category number of a map $f\colon X\to Y$ with basic results about this numerical invariant. For instance, we explore the injective category number under pullbacks and compositions. In the case that $f$ is the quoti
Externí odkaz:
http://arxiv.org/abs/2405.04317
In this paper, for fibrations $p:E\to B$, $p':E'\to B$ over $B$ and a free involution $\tau:E\to E$ which satisfy the equality $p\circ\tau=p$, we discover a connection between the sectional category of the double covers $q:E\to E/\tau$ and $q^Y:F_{p'
Externí odkaz:
http://arxiv.org/abs/2404.04470
Autor:
Zapata, Cesar A. Ipanaque
A classic problem in analysis is to solve nonlinear equations of the form \begin{equation*} F(x)=0, \end{equation*} where $F:D^n\to \mathbb{R}^m$ is a continuous map of the closed unit disk $D^n\subset\mathbb{R}^n$ in $\mathbb{R}^m$. A topological te
Externí odkaz:
http://arxiv.org/abs/2403.18848
In this paper we discover a connection between the Milnor fibration theory and current research trends in topological robotics. The configuration space and workspace are often described as subspaces of some Euclidean spaces. The work map is a continu
Externí odkaz:
http://arxiv.org/abs/2401.11015
Let $G$ be a finite group with order $|G|=\ell$ and $2\leq q\leq \ell$. For a free $G$-space $X$, we introduce a notion of $q$-th index of $(X,G)$, denoted by $\text{ind}_q(X,G)$. Our concept is relevant in the Borsuk-Ulam theory. We draw general est
Externí odkaz:
http://arxiv.org/abs/2312.11957
In this paper, we introduce the notion of transversal topological complexity (TTC) for a smooth manifold $X$ with respect to a submanifold of codimension 1 together with basic results about this numerical invariant. In addition, we present several ex
Externí odkaz:
http://arxiv.org/abs/2303.06715
The higher topological complexity of a space $X$, $\text{TC}_r(X)$, $r=2,3,\ldots$, and the topological complexity of a map $f$, $\text{TC}(f)$, have been introduced by Rudyak and Pave\v{s}i\'{c}, respectively, as natural extensions of Farber's topol
Externí odkaz:
http://arxiv.org/abs/2212.03441