A topological proof of the Grothendieck formula in real algebraic geometry.
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.
scientific article; zbMATH DE number 2028626