Topological degree and quadratic forms (Q1304906)

The author gives explicit expressions for the topological degree and its parity for polynomial mappings of \({\mathbb R}^n\to {\mathbb R}^n\) or, more generally, between real algebraic \(n\)-dimensional varieties via signatures of quadratic forms over real polynomial local algebras. The proofs are essentially based on the Eisenbud-Levine formula [\textit{D. Eisenbud} and \textit{H. I. Levine}, Ann. Math. (2) 106, 19-44 (1977; Zbl 0398.57020)].