Rigidity for prelegendrians via Legendrian Contact Homology

par Álvaro del Pino Gómez (Universiteit Utrecht)

vendredi 19 déc. 2025, 11:15 → 12:15 Europe/Paris

112 (ICJ)

Given a pair of numbers $(k,m)$, one can study maximally non-integrable distributions of rank $k$ in $m$-dimensional manifolds. The most studied case is $(2n,2n+1)$, contact topology. The other classic case is $(2n-1,2n)$, the study of even-contact structures, whose homotopy classification was settled by McDuff. Other cases (e.g. $(2,4), (2,5), (4,6),..$.) have been studied in the last few years from the perspective of the $h$-principle.  Often one studies not just the structures themselves, but also the submanifolds that interact nicely with them (typically being transverse or tangent).

In this talk I will discuss a rigidity phenomenon in the study of $(4,6)$ distributions (as far as I know, the first such result outside of contact topology). Namely, I will exhibit a family of submanifolds in the "standard elliptic $(4,6)$ distribution" in $\mathbb{R}^6$, all of which are distinct up to homotopy despite being formally equivalent. That is, the $h$-principle fails for these submanifolds (which we call prelegendrians). The main idea is that one can relate these objects to legendrians in a $7$-dimensional contact manifold, and then apply legendrian contact homology. This is joint work with Wei Zhou and Eduardo Férnandez.