Higher-dimensional contact topology

April 15 to April 19, 2024

at the

American Institute of Mathematics, Pasadena, California

organized by

Roger Casals, Yakov Eliashberg, Ko Honda, and Gordana Matic

Original Announcement

This workshop will focus on the development of higher-dimensional contact topology, with a focus on convex hypersurface theory and contact submanifolds. We will bring a diverse group of experts, spanning a variety of career stages, and represent the different research interests from the international community of researchers in contact topology.

The first aim of the workshop is to develop and apply convex hypersurface theory so as to discover new results in higher-dimensional contact topology. This is motivated by recent works which open the floor to tackling problems in higher-dimensional contact topology that previously seemed inaccessible. Many geometric objects in lower-dimensional convex surfaces, such as divides and bypasses, can be effectively manipulated so as to classify (germs of) contact structures near a convex surface. Part of the workshop shall focus on establishing these results in higher dimensions and discovering how to manipulate convex hypersurfaces. In particular, this also involves the study of the dynamics of the involved vector fields. In particular, this includes:

  1. Develop the relationship between Convex Hypersurface Theory and the problem of Weinstein fillability of contact manifolds, and determine ways in which Convex Hypersurface Theory can be used for the classification of contact structures in higher-dimensional contact manifolds.
  2. Develop and apply parametric Convex Hypersurface Theory and study of the dynamics of Liouville vector fields in higher dimensions.
The second aim of this workshop is to broaden and deepen the study of higher-dimensional contact submanifolds, the natural higher-dimensional counter-part to transverse knots. Following recent developments, the first steps for a rich theory of contact divisors (codimension-2 contact submanifolds) have now been established. In particular, existence is now understood, as it is the fact that the same smooth isotopy class can be often represented by different (even infinitely many) contact isotopy classes. This opens a long series of interesting questions, many of which we believe can be addressed using currently available methods, or by suitably developing some of the recent ideas in the field further. In particular, we hope to:

  1. Develop new constructions for contact submanifolds which are smoothly isotopic but not contact isotopic, as well as methods to distinguish them.
  2. Study the applications of bypasses in higher dimensions.

Material from the workshop

A list of participants.

The workshop schedule.

A report on the workshop activities.

A list of open problems.

Workshop videos