Pinwheels as Lagrangian barriers

2022/10/01 by Brendel, Joé, Schlenk, Felix
#FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2210.00280

Abstract

The complex projective plane CP² contains certain Lagrangian CW-complexes called pinwheels, which have interesting rigidity properties related to solutions of the Markov equation. We compute the Gromov width of the complement of pinwheels and show that it is strictly smaller than the Gromov width of CP², meaning that pinwheels are Lagrangian barriers in the sense of Biran. The accumulation points of the set of these Gromov widths are in a simple bijection with the Lagrange spectrum below 3.

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