Mapping degree and Euler characteristic

Abstract

Let V_δ denote a local level surface for function-germ f : (Rⁿ⁺¹,0) → (R,0). A mapping degree formula for difference of the Euler characteristics of V_δ ∩ {g ≤ 0} and V_δ ∩ {g ≥ 0} is given, when level surfaces of a function g : (Rⁿ⁺¹,0) → (R,0) are parallelizable.