$h$-Principle for Maximal Growth Distributions

Description

The existence and classification problem for maximal growth distributions on smooth manifolds has garnered much interest in the mathematical community in recent years. Prototypical examples of maximal growth distributions are contact structures on $3$-dimensional manifolds and Engel distributions on $4$-dimensional manifolds. The existence and classification of maximal growth distributions on open manifolds follows from Gromov’s $h$-Principle for open manifolds. Nonetheless, not so much was known for the case of closed manifolds and several open questions have been posed in the literature throughout the years about this problem.

In our recent work [1] we show that maximal growth distributions of rank $> 2$ abide by a full h-principle in all dimensions, providing thus a classification result from a homotopic viewpoint. As a consequence we answer in the positive, for $k > 2$, the long-standing open question posed by M. Kazarian and B. Shapiro more than 25 years ago of whether any parallelizable manifold admits a $k$-rank distribution of maximal growth.

[1]. Martínez-Aguinaga, Javier. Existence and classification of maximal growth distributions . Preprint. arXiv:2308.10762

Speaker

Profesor ayudante, Departamento de Álgebra, Geometría y Topología

www.mat.ucm.es/decanato/cvs/AGT/cvFJMM.pdf