A topological proof of the Grothendieck formula in real algebraic geometry.
type: Item
instance of: scholarly article
title: A topological proof of the Grothendieck formula in real algebraic geometry.
zbMATH Open document ID: 1076.14080
author: Jacek Bochnak
author: Wojciech Kucharz
published in: L'Enseignement Mathématique. 2e Série
publication date: 2002-01-01T00:00:00Z
review text: As is known [see \textit{R. Benedetti} and \textit{M. Dedò}, Compos. Math. 53, 143--151 (1984; Zbl 0547.14019)], if \(X\) is a compact nonsingular real algebraic set, and \(v\) a cohomology class in \(H^2(X; \mathbb{Z}/2)\) whose Poincaré dual homology class can be represented by an algebraic subset of \(X\), then there exists an algebraic vector bundle \(\xi\) on \(X\) such that \(w_1(\xi)= 0\) and \(w_2(\xi)= v\), where \(w_i(\xi)\) is the \(i\)th Stiefel-Whitney class of \(\xi\). The goal of the present article is to give a self-contained topological proof of the statement formulated above.
Mathematics Subject Classification ID: 14P25
zbMATH DE Number: 2028626
reviewed by: Ilia Itenberg
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2028626