On Topological Invariants Associated With a Polynomial With Isolated Critical Points

Abstract

Abstract. We consider a polynomial f : ‫ޒ‬ n → ‫ޒ‬ with isolated critical points and we relate χ (f −1 (0)) and χ ({f ≥ 0}) − χ ({f ≤ 0}) to the topological degrees of polynomial maps defined in terms of f .2000 Mathematics Subject Classification. 14P25.

Topology and geometry of real singularities

“…2 lie in {≤, ≥}. In [17,22] we gave generalizations in some cases where W admits isolated singularities. However, in general when W is not compact, we do not have any signature formula neither for χ(W ) nor for χ(W ∩ {G 1 ?…”