Constructions in symplectic and contact topology via h-principles

Certain `flexible' structures in symplectic and contact topology satisfy h-principles, meaning that their geometry reduces to underlying topological data. Although these flexible structures have no interesting geometry by themselves, I will show how h-principles provide a unified approach to various constructions in symplectic and contact topology and can be used to build new exotic structures that are geometrically interesting. More precisely, I will explain how to use h-principles to construct contact manifolds with many Weinstein fillings in high dimensions, prove that all contact manifolds have symplectic caps, and construct exotic cotangent bundles containing many closed exact Lagrangians.

Date

Speakers

Oleg Lazarev

Affiliation

Columbia University