Pinwheels as Lagrangian barriers

Abstract: Pinwheels are certain singular Lagrangians in four-dimensional symplectic manifolds. In this talk we focus on the case of the complex projective plane, where pinwheels arise naturally as visible Lagrangians in its almost toric fibrations or, alternatively, as vanishing cycles of its degenerations. Pinwheels have been shown to have interesting rigidity properties by Evans--Smith. The goal of this talk is to show that Lagrangian pinwheels are Lagrangian barriers in the sense of Biran, meaning that their complement has strictly smaller Gromov width than the ambient space. Furthermore, we will discuss a connection to the Lagrange spectrum. This is joint work with Felix Schlenk.

differential geometrydynamical systemsgeometric topologysymplectic geometryspectral theory

Audience: researchers in the topic

Geometry and Dynamics seminar

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