Stratified critical points one the real Milnor fibre and integral-geometric formulas

Abstract

Let $(X,0)\subset ({\mathbb{R}}^n,0)$ be the germ of a closed subanalytic set and let $f$ and $g:(X,0)\to (\mathbb{R},0)$ be two subanalytic functions. Under some conditions, we relate the critical points of $g$ on the real Milnor fibre $X\cap f^{-1}(\delta )\cap B_{\epsilon }$, $0<|\delta |\ll \epsilon \ll 1$, 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.

Cited by in corpus (1)

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