The neighborhood of a leaf of a singular foliation

Abstract: Near a leaf, regular foliations are classified by their monodromies. What about the singular leaves of singular foliations? The first point is that for a singular leaf, there is a transverse singular foliation, which is constant all along the leaf. In a previous work, Leonid Ryvkin and I have proven that for simply connected singular leaves with a certain type of transverse singular foliations, there is only one possiblity: the direct product. Here, we present a complete classification at the formal level, which is composed of two parts: a sort of monodromy and a finite dimensional principal bundle. We use a presentation where Yang-Mills bundles (as introduced by Kotov and Strobl) play a central role. Joint work with Simon Raphael Fischer (Taipei).

mathematical physicsalgebraic topologydifferential geometryrepresentation theorystatistics theory

Audience: researchers in the topic

( slides | video )

Prague-Hradec Kralove seminar Cohomology in algebra, geometry, physics and statistics

Series comments: Virtual coffee starts on Zoom already 15 minutes before the seminar.