Topological formulas for closed semi-algebraic sets by Euler integration

被引：1

作者：

Dutertre, N. ^{[1
]}

Moya-Perez, J. A. ^{[1
]}

机构：

[1] Aix Marseille Univ, CNRS, Cent Marseille, I2M,UMR 7373, F-13453 Marseille, France

来源：

REAL AND COMPLEX SINGULARITIES | 2016年 / 675卷

关键词：

Semi-algebraic sets; Euler integration;

D O I：

10.1090/conm/675/13585

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper is divided in two parts. In the first one, we consider a polynomial function f :R-n -> R with a finite number of critical points and we give a formula that relates its index at infinity to Euler characteristics of links at infinity, using Euler integration theory. In the second one, we generalize this result by considering a closed semi-algebraic set X and a C-2 semi-algebraic function f : R-n -> R such that f|x has a finite number of critical points.

引用

页码：89 / 102

页数：14

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