On the sequential topological complexity of group homomorphisms

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2024-08-16 DOI:10.1016/j.topol.2024.109045

Nursultan Kuanyshov

引用次数: 0

Abstract

We define and develop a homotopy invariant notion for the sequential topological complexity of a map $f : X \to Y$ , denoted $T C_{r} (f)$ , that interacts with $T C_{r} (X)$ and $T C_{r} (Y)$ in the same way Jamie Scott's topological complexity map $T C (f)$ interacts with $T C (X)$ and $T C (Y)$ . Furthermore, we apply $T C_{r} (f)$ to studying group homomorphisms $ϕ : Γ \to Λ$ .

In addition, we give the characterization of cohomological dimension of group homomorphisms.

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论群同态的顺序拓扑复杂性

我们定义并发展了一个同调不变的概念，即映射 f:X→Y 的序列拓扑复杂性，记为 TCr(f)，它与 TCr(X) 和 TCr(Y) 交互作用的方式与杰米-斯科特的拓扑复杂性映射 TC(f) 与 TC(X) 和 TC(Y) 交互作用的方式相同。此外，我们还将 TCr(f) 应用于研究群同态 j:Γ→Λ。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Topology and its Applications 数学-数学

CiteScore

1.20

自引率

33.30%

发文量

251

审稿时长

6 months

期刊介绍： Topology and its Applications is primarily concerned with publishing original research papers of moderate length. However, a limited number of carefully selected survey or expository papers are also included. The mathematical focus of the journal is that suggested by the title: Research in Topology. It is felt that it is inadvisable to attempt a definitive description of topology as understood for this journal. Certainly the subject includes the algebraic, general, geometric, and set-theoretic facets of topology as well as areas of interactions between topology and other mathematical disciplines, e.g. topological algebra, topological dynamics, functional analysis, category theory. Since the roles of various aspects of topology continue to change, the non-specific delineation of topics serves to reflect the current state of research in topology. At regular intervals, the journal publishes a section entitled Open Problems in Topology, edited by J. van Mill and G.M. Reed. This is a status report on the 1100 problems listed in the book of the same name published by North-Holland in 1990, edited by van Mill and Reed.