Euler obstruction and Lipschitz-Killing curvatures

Nicolas Dutertre (1, 2)

1 I2M - Institut de Mathématiques de Marseille
2 LAREMA - Laboratoire Angevin de Recherche en Mathématiques

Applying a local Gauss-Bonnet formula for closed subanalytic sets to the complex analytic case, we obtain characterizations of the Euler obstruction of a complex analytic germ in terms of the Lipschitz-Killing curvatures and the Chern forms of its regular part. We also prove analogous results for the global Euler obstruction. As a corollary, we give a positive answer to a question of Fu on the Euler obstruction and the Gauss-Bonnet measure.

Mots clés: Euler obstruction; constructible functions; complex link; Lipschitz-Killing curvatures

Domaines: Géométrie algébrique [math.AG]; Géométrie différentielle [math.DG]

Nicolas Dutertre. Euler obstruction and Lipschitz-Killing curvatures. Israel Journal of Mathematics, 2016, 213, pp.109-137. ⟨10.1007/s11856-016-1322-9⟩. ⟨hal-00995743⟩