Dept Math & Stat UiT, Forskningsparken B459
  16 Mar 2023 Thu 14:00-15:00

Igor Zelenko (Texas A&M University)

"Gromov's h-principle for corank two distribution of odd rank with maximal first Kronecker index"

While establishing various versions of the h-principle for contact distributions (Eliashberg (1989) in dimension 3, Borman-Eliashberg-Murphy (2015) in arbitrary dimension), and even-contact contact (D. McDuff, 1987) distributions are among the most remarkable advances in differential topology in the last four decades, very little is known about analogous results for other classes of distributions, e.g. generic distributions of corank 2 or higher. The smallest dimensional nontrivial case of corank 2 distributions are Engel distributions, i.e. the maximally nonholonomic rank 2 distributions on 4-manifolds. This case is highly nontrivial and was treated recently by Casals-Perez-del Pino-Presas (2017).

In my talk, I will show how to use the method of convex integration in order to establish all versions of the h-principle for corank 2 distributions of arbitrary odd rank satisfying a natural generic assumption on the associated pencil of skew-symmetric forms. During the talk, I will try to give all the necessary background related to the method of convex integration in principle. This is the joint work with Milan Jovanovic, Javier Martinez-Aguinaga, and Alvaro del Pino.