Constructions in symplectic and contact topology via h-principles

Constructions in symplectic and contact topology via h-principles

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Oleg Lazarev, Columbia University
IAS - Simonyi Hall Seminar Room SH-101

Certain `flexible' structures in symplectic and contact topology satisfy h-principles, meaning that their geometry reduces to underlying topological ata. 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.