April 25, 2025
Title: The h-principle fails for prelegendrians in elliptic distributions
Speaker: Álvaro del Pino Gómez
The main question in the topological theory of distributions asks: "Are there other classes of maximally non-integrable distributions, apart from contact structures, for which the h-principle fails?". In more down to earth terms: "Are there invariants of distributions that go beyond the obvious ones?", "Is there an interesting theory that is not just algebraic topological in nature?".
This question is at the moment wide open. All progress has gone in the opposite direction: proving that various classes of distributions are classified by their obvious algebraic topological invariants.
The aim of the talk is twofold: First, I will explain the general landscape of the field, giving an overview of what we know. Then, I will explain a recent result with Wei Zhou and Eduardo Fernández that says: There is a family of submanifolds (so called prelegendrians), adapted to a certain family of distributions (called elliptic), that do have non-obvious invariants. These invariants come from Contact Topology, thanks to the following key fact: elliptic distributions can be "contactised", producing an associated contact structure.