Fundamental class of real algebraic sets

✍ Scribed by Zbigniew Szafraniec

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 95 KB
• Volume: 111
• Category: Article
• ISSN: 0166-8641
• DOI: 10.1016/s0166-8641(99)00207-2

✦ Synopsis

Let F : R n → R k (n k) be a polynomial mapping such that the real algebraic set X = F -1 (0) is compact. There are introduced a fundamental class [X] F ∈ H n-k (X; Z) and a topological degree deg(G) for G : X → R n-k+1 -{0}, which coincide with the usual ones when X is a smooth oriented m-manifold. There is also given an effective method for computing deg(G) and a formula for the degree on critical points of mappings Q : X → R n-k .