(LDT seminar) Non-flexible loops of loose Legendrians in 3 dimensions

In recent years, significant progress has been made in understanding families of Legendrians in 3-dimensional contact topology. For instance, the homotopy type of the component of the max-tb Legendrian unknot (or any algebraic link) in the standard contact 3-sphere is now completely understood. However, the existence of non-flexible families of Legendrians has remained an open question. In this talk, we will explore this question in the context of loops of Legendrians. Specifically, we will show that in every closed overtwisted contact 3-manifold, there exists a non-contractible yet formally contractible loop of loose Legendrians. The proof relies on h-principles and parametrized Legendrian surgery, drawing inspiration from Dave Gay’s work on diffeomorphisms of the 4-sphere. This talk is based on joint work in progress with Fabio Gironella.