欧拉阻塞、布拉塞莱数和临界点

IF 1.2 3区数学 Q1 MATHEMATICS Research in the Mathematical Sciences Pub Date : 2024-03-22 DOI:10.1007/s40687-024-00426-1

Nicolas Dutertre

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引用次数: 0

摘要

我们将定义在复解析集合上的复解析函数-胚的布拉塞莱数与它的实部在链接正则位置上的临界点联系起来。同样，我们给出了欧拉阻塞的新特征，即一般实线上投影的链接正则部分上的临界点。作为推论，我们得到了傅氏猜想的欧拉阻碍与高斯-波奈度量之间关系的新证明。

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Euler obstruction, Brasselet number and critical points

We relate the Brasselet number of a complex analytic function-germ defined on a complex analytic set to the critical points of its real part on the regular locus of the link. Similarly we give a new characterization of the Euler obstruction in terms of the critical points on the regular part of the link of the projection on a generic real line. As a corollary, we obtain a new proof of the relation between the Euler obstruction and the Gauss–Bonnet measure, conjectured by Fu.

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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.

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