Date/heure
30 septembre 2021
14:15 - 15:15
Oratrice ou orateur
Sergiu Moroianu (Académie roumaine des sciences)
Catégorie d'évènement Séminaire Théorie de Lie, Géométrie et Analyse
Résumé
This talk will start with a survey of the standard Gauss-Bonnet formula on surfaces and its extension to higher dimensions, including on manifolds with corners, and more generally on polyhedral Riemannian manifolds.
I will then introduce transgressions of arbitrary order, with respect to families of unit-vector fields indexed by a polytope, for the Pfaffian of the curvature of metric connections on real vector bundles. They allow one to compute the Euler characteristic of a Riemannian polyhedral manifold in terms of integrals of explicit transgression forms on each boundary face, extending Chern’s differential-geometric proof of the generalized Gauss-Bonnet formula on closed manifolds and on manifolds-with-boundary.
As a consequence, I will give an identity for spherical and hyperbolic polyhedra relating volumes of faces of even codimension and measures of outer angles.
Based on https://arxiv.org/abs/2011.06538