流形上光滑函数的里伯空间 II

IF 1.2 3区数学 Q1 MATHEMATICS

Research in the Mathematical Sciences Pub Date : 2024-03-14 DOI:10.1007/s40687-024-00436-z

Osamu Saeki

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引用次数: 0

摘要

拓扑空间上连续函数的里布空间是水平集的连通分量空间。在本文中，我们描述了封闭流形上那些其里布空间具有有限图结构的光滑函数的特征。我们还给出了几个封闭流形上光滑函数的明确例子，这些函数本身或它们的里布空间具有一些有趣的性质。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Reeb spaces of smooth functions on manifolds II

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Reeb spaces of smooth functions on manifolds II

The Reeb space of a continuous function on a topological space is the space of connected components of the level sets. In this paper we characterize those smooth functions on closed manifolds whose Reeb spaces have the structure of a finite graph. We also give several explicit examples of smooth functions on closed manifolds such that they themselves or their Reeb spaces have some interesting properties.

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来源期刊

Research in the Mathematical Sciences Mathematics-Computational Mathematics

CiteScore

2.00

自引率

8.30%

发文量

期刊介绍： Research in the Mathematical Sciences is an international, peer-reviewed hybrid journal covering the full scope of Theoretical Mathematics, Applied Mathematics, and Theoretical Computer Science. The Mission of the Journal is to publish high-quality original articles that make a significant contribution to the research areas of both theoretical and applied mathematics and theoretical computer science. This journal is an efficient enterprise where the editors play a central role in soliciting the best research papers, and where editorial decisions are reached in a timely fashion. Research in the Mathematical Sciences does not have a length restriction and encourages the submission of longer articles in which more complex and detailed analysis and proofing of theorems is required. It also publishes shorter research communications (Letters) covering nascent research in some of the hottest areas of mathematical research. This journal will publish the highest quality papers in all of the traditional areas of applied and theoretical areas of mathematics and computer science, and it will actively seek to publish seminal papers in the most emerging and interdisciplinary areas in all of the mathematical sciences. Research in the Mathematical Sciences wishes to lead the way by promoting the highest quality research of this type.