重新审视相对断面类别

IF 0.8 4区数学 Q2 MATHEMATICS

Expositiones Mathematicae Pub Date : 2024-07-11 DOI:10.1016/j.exmath.2024.125590

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引用次数: 0

摘要

相对截面范畴的概念是对经典截面范畴理论的扩展，它包含了纤维沿映射的回拉。我们的论文不仅要探索这一扩展，还要深入研究其性质。我们试图揭示相对截面范畴如何统一近期文献中发现的几个同位数值不变式。这些变量包括穆里略-吴（Murillo-Wu）或斯科特（Scott）定义的映射拓扑复杂性、法伯（Farber）定义的相对拓扑复杂性，以及马西亚斯-维尔戈斯（Macías-Virgós）和莫斯克拉-罗伊斯（Mosquera-Lois）意义上的连续映射同位距离等。

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Relative sectional category revisited

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. We seek to uncover how the relative sectional category unifies several homotopic numerical invariants found in recent literature. These include the topological complexity of maps according to Murillo–Wu or Scott, relative topological complexity as defined by Farber, and homotopic distance for continuous maps in the sense of Macías-Virgós and Mosquera-Lois, among others.

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来源期刊

Expositiones Mathematicae 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

40 days

期刊介绍： Our aim is to publish papers of interest to a wide mathematical audience. Our main interest is in expository articles that make high-level research results more widely accessible. In general, material submitted should be at least at the graduate level.Main articles must be written in such a way that a graduate-level research student interested in the topic of the paper can read them profitably. When the topic is quite specialized, or the main focus is a narrow research result, the paper is probably not appropriate for this journal. Most original research articles are not suitable for this journal, unless they have particularly broad appeal.Mathematical notes can be more focused than main articles. These should not simply be short research articles, but should address a mathematical question with reasonably broad appeal. Elementary solutions of elementary problems are typically not appropriate. Neither are overly technical papers, which should best be submitted to a specialized research journal.Clarity of exposition, accuracy of details and the relevance and interest of the subject matter will be the decisive factors in our acceptance of an article for publication. Submitted papers are subject to a quick overview before entering into a more detailed review process. All published papers have been refereed.