Euler obstruction and indices of vector fields
type: Item
instance of: scholarly article
title: Euler obstruction and indices of vector fields
zbMATH Open document ID: 0983.32030
DOI: 10.1016/S0040-9383(99)00009-9
author: Dũng Tráng Lê
author: Jean-Paul Brasselet
author: José Seade
published in: Topology
publication date: 2001-09-30T00:00:00Z
review text: Let \((X,0)\subset (\mathbb{C}^N,0)\) be the germ of an equidimensional complex analytic singularity and \(V_i\) \(1\leq i\leq x\), the connected strata of a Whitney stratification of a small representative of \((X,0)\). Here the authors prove the existence of a Zariski open dense subset \(\Omega\) in the space of complex linear forms on \(\mathbb{C}^N\) such that for every \(f\in\Omega\) there is \(\varepsilon_0>0\) such that for any \(\varepsilon\) with \(0<\varepsilon < \varepsilon_0\) and \(t\neq 0\) sufficiently small \[ Eu(X,0)= \sum_{1\leq i\leq x}\chi \bigl(V_i\cap {\mathbf B}_\varepsilon\cap f^{-1}(t) \bigr)Eu_{V_i}(X) \] where \(Eu (X,0)\) is the Euler obstruction of \(X\) at 0, \({\mathbf B}_\varepsilon\) is the \(\varepsilon\)-ball around \(0,\chi\) denotes the Euler-Poincaré characteristic and \(Eu_{V_i}(X)\) is the value of the Euler obstruction of \(X\) at any point of \(V_i\).
reviewed by: E. Ballico
Mathematics Subject Classification ID: 32S10
Mathematics Subject Classification ID: 32S05
Mathematics Subject Classification ID: 32S50
Mathematics Subject Classification ID: 32S60
Mathematics Subject Classification ID: 14J17
Mathematics Subject Classification ID: 14F05
Mathematics Subject Classification ID: 57R25
zbMATH DE Number: 1526236
zbMATH Keywords: stratified vector field
zbMATH Keywords: hyperplane section
zbMATH Keywords: radial vector field
zbMATH Keywords: index of a vector field
zbMATH Keywords: vector field on a complex space
zbMATH Keywords: complex analytic singularity
zbMATH Keywords: Whitney stratification
zbMATH Keywords: Euler obstruction
MaRDI profile type: Publication
full work available at URL: s0040-9383(99)00009-9
OpenAlex ID: W2012868913
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description: scientific article; zbMATH DE number 1526236