Theses
THESIS DEFENSE -- Flexibility and rigidity for maximally non-integrable distributions
Speaker: Wei Zhou ()Advisor/s: Eduardo Fernández (Georgia Tech), Álvaro del Pino (Utrecht University), Francisco Presas (ICMAT-CSIC)Date: Friday, 06 February 2026 - 15:00Place: Sala de Grados (250C), Facultad de CC. Matemáticas, Universidad Complutense de Madrid
Abstract:
This thesis studies rigidity phenomena for non-integrable distributions beyond the contact setting. We focus on fat distributions, maximally non-integrable distributions that generalize contact structures to higher corank and admit natural symplectizations and contactizations. We introduce prelegendrian submanifolds, characterized by the existence of a canonical Legendrian lift to the contactization.
Our main results show: (1) there are infinitely many exotic prelegendrian embeddings in the standard corank-2 fat space C^2n+1, all formally isotopic but pairwise non-isotopic, distinguished by pseudoholomorphic-curve invariants of their Legendrian lifts; and (2) a notion of prelegendrian stabilization producing loose Legendrian lifts, yielding further families of exotic prelegendrians. To the best of our knowledge, these are the first rigidity results at the submanifold level for maximally non-integrable distributions beyond the contact case, where such rigidity phenomena were previously only known for Legendrians in contact manifold.
