Zobrazeno 1 - 10
of 594
pro vyhledávání: '"55M30"'
In this paper, we compute sharp bounds for the higher topological complexity of many planar polygon spaces having small genetic codes. In most of these cases we show that the $k$-th higher topological complexity of planar polygon spaces is either $km
Externí odkaz:
http://arxiv.org/abs/2412.01529
The Lusternik-Schnirelmann category of a space was introduced to obtain a lower bound on the number of critical points of a $C^1$-function on a given manifold. Related to Lusternik-Schnirelmann category and motivated by topological robotics, the topo
Externí odkaz:
http://arxiv.org/abs/2411.01980
Autor:
Chen, Weiyan, Gu, Xing
We study the topological complexity, in the sense of Smale, of three enumerative problems in algebraic geometry: finding the 27 lines on cubic surfaces, the 28 bitangents and the 24 inflection points on quartic curves. In particular, we prove lower b
Externí odkaz:
http://arxiv.org/abs/2411.00497
Let $X$ be a $G$-space. In this paper, we introduce the notion of sectional category with respect to $G$. As a result, we obtain $G$-homotopy invariants: the LS category with respect to $G$, the sequential topological complexity with respect to $G$ (
Externí odkaz:
http://arxiv.org/abs/2410.00139
Autor:
İs, Melih, Karaca, İsmet
We define digital $m-$homotopic distance and its higher version. We also mention related notions such as $m-$category in the sense of Lusternik-Schnirelmann and $m-$complexity in topological robotics. Later, we examine the homotopy invariance or $m-$
Externí odkaz:
http://arxiv.org/abs/2408.15596
Autor:
Jauhari, Ekansh
Recently, a new homotopy invariant of metric spaces, called the distributional LS-category, was defined, which provides a lower bound to the classical LS-category. In this paper, we obtain several sufficient conditions for the distributional LS-categ
Externí odkaz:
http://arxiv.org/abs/2408.11036
We introduce and study the proper topological complexity of a given configuration space, a version of the classical invariant for which we require that the algorithm controlling the motion is able to avoid any possible choice of ``unsafe'' area. To m
Externí odkaz:
http://arxiv.org/abs/2407.16679
Autor:
Jauhari, Ekansh
We develop the theory of the intertwining distributional versions of the LS-category and the sequential topological complexities of a space $X$, denoted by $\mathsf{icat}(X)$ and $\mathsf{iTC}_m(X)$, respectively. We prove that they satisfy most of t
Externí odkaz:
http://arxiv.org/abs/2406.12265
Autor:
Daundkar, Navnath
In this paper, we define and study an equivariant analogue of Cohen, Farber and Weinberger's parametrized topological complexity. We show that several results in the non-equivariant case can be extended to the equivariant case. For example, we establ
Externí odkaz:
http://arxiv.org/abs/2405.20809
Autor:
Calcines, Jose Manuel Garcia
The concept of relative sectional category expands upon classical sectional category theory by incorporating the pullback of a fibration along a map. Our paper aims not only to explore this extension but also to thoroughly investigate its properties.
Externí odkaz:
http://arxiv.org/abs/2405.19924