Floer cohomology of Platonic Lagrangians

We analyse holomorphic discs on Lagrangian $\mathrm{SU}(2)$-orbits in a family of quasihomogeneous threefolds of $\mathrm{SL}(2, \mathbb{C})$, previously studied by Evans–Lekili, introducing several techniques that should be applicable to wider classes of homogeneous Lagrangians. By studying the closed–open map we place strong restrictions on the self-Floer cohomology of these Lagrangians, which we then compute using the Biran–Cornea pearl complex.

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Received 9 November 2015

Accepted 11 July 2018

Published 26 July 2019