Service interruption on Monday 11 July from 12:30 to 13:00: all the sites of the CCSD (HAL, Epiciences, SciencesConf, AureHAL) will be inaccessible (network hardware connection).
Skip to Main content Skip to Navigation
Journal articles

Stratified critical points on 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 $g : (X,0) \rightarrow (\mathbb{R},0)$ be two subanalytic functions. Under some conditions, we relate the critical points of $g$ on the real Milnor fibre $X \cap f^{-1}(\delta) \cap B_\epsilon$, $0 < \vert \delta \vert \ll \epsilon \ll 1$, 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.
Complete list of metadata

Cited literature [9 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-00848992
Contributor : Nicolas Dutertre Connect in order to contact the contributor
Submitted on : Monday, July 29, 2013 - 4:38:49 PM
Last modification on : Thursday, October 21, 2021 - 3:59:31 AM
Long-term archiving on: : Wednesday, October 30, 2013 - 4:12:52 AM

Files

DutertreProcTrotman.pdf
Files produced by the author(s)

Identifiers

Citation

Nicolas Dutertre. Stratified critical points on the real Milnor fibre and integral-geometric formulas. Journal of Singularities, Worldwide Center of Mathematics, LLC, 2015, 13, pp.20. ⟨10.5427/jsing.2015.13e⟩. ⟨hal-00848992⟩

Share

Metrics

Record views

234

Files downloads

419