February 5, 2021
Title: On the homotopy type of the contactomorphism group of a tight contact 3-manifold
Speaker: Eduardo Fernandez (Junior talk, 5:30pm)
One of the building blocks in the study of the homotopy type of the diffeomorphism group of a 3-manifold is the positive answer of A. Hatcher to the Smale conjecture. This result has its contact counterpart: Eliashberg's theorem about the contractibility of the contactomorphism group of the tight contact 3–ball.
In order to adapt the smooth techniques to the contact world, it is necessary to develop an understanding of the space of embeddings of surfaces into a given tight contact 3-manifold. In this talk we will see how to do this for simple surfaces such as disks and spheres. As a consequence, we will conclude that, with the exception of connected components, all the remaining homotopy groups of the group of contactomorphisms of a tight contact 3-manifold are controlled by topological invariants.
This talk is a continuation of the previous talk "Flexibility in contact 3-manifolds: from contactomorphisms to legendrian knots" by Javier Martínez-Aguinaga. Joint work with Javier Martínez-Aguinaga and Fran Presas.