TL;DR
This paper investigates the Floer cohomology of specific homogeneous Lagrangian submanifolds in complex threefolds, introducing new techniques for analyzing holomorphic discs and computing self-Floer cohomology.
Contribution
It develops methods to study holomorphic discs on SU(2)-orbits and computes their Floer cohomology, extending understanding of homogeneous Lagrangians.
Findings
Restrictions on self-Floer cohomology of these Lagrangians
Application of the closed-open map to derive cohomology properties
Explicit computation of Floer cohomology using pearl complex
Abstract
We analyse holomorphic discs on Lagrangian SU(2)-orbits in a family of quasihomogeneous threefolds of SL(2, 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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