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arXiv · 1307.7604

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

Nicolas Dutertre
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Abstract

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

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Nicolas Dutertre. 2013-07-29. Stratified critical points one the real Milnor fibre and integral-geometric formulas. https://arxiv.org/abs/1307.7604

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