Stratified critical points on the real Milnor fibre and integral-geometric formulas
نویسندگان
چکیده
Let (X, 0) ⊂ (R, 0) be the germ of a closed subanalytic set and let f and g : (X, 0) → (R, 0) be two subanalytic functions. Under some conditions, we relate the critical points of g on the real Milnor fibre X ∩ f(δ)∩Bǫ, 0 < |δ| ≪ ǫ ≪ 1, to the topology of this fibre and other related subanalytic sets. As an application, when g is a generic linear function, we obtain an “asymptotic” Gauss-Bonnet formula for the real Milnor fibre of f . From this Gauss-Bonnet formula, we deduce “infinitesimal” linear kinematic formulas.
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