SEMINARIO DE GEOMETRIA

Title: The classification problem for (4,6)-bracket-generating structures

Speaker: Javier Martínez-Aguinaga (ICMAT-UCM)

Date: miércoles, 13 de Enero, 16:00
Place:  Online - https://zoom.us/j/2203382215

Abstract: The classification problem for bracket–generating distributions in differentiable manifolds
from a homotopic viewpoint has been tackled for certain cases.

Gromov classified contact structures up to homotopy in open manifolds. Afterwards, a subclass of this type of structures called overtwisted were classified in closed manifolds up to isotopy, first by Eliashberg in dimension 3 and later on by Borman, Eliashberg and Murphy in all dimensions. McDuff classified even-contact structures in even-dimensional manifolds, showing that there exists a full h-principle.

More recently, Casals, del Pino, Pérez and Presas proved an existenceh−principle for Engel structures in smooth 4−manifolds. On the other hand, del Pino and Vogel showed that there exists a full h−principle when restricted to the subclass of overtwisted Engel structures.

In this talk we will discuss the classification problem for (4,6)−bracket–generating structures through convex integration. This is work in progress with Alvaro del Pino (Utrecht University).