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Monotone Lagrangians in cotangent bundles of spheres (2011.13478v2)

Published 26 Nov 2020 in math.SG

Abstract: We study the compact monotone Fukaya category of $T*Sn$, for $n\geq 2$, and show that it is split-generated by two classes of objects: the zero-section $Sn$ (equipped with suitable bounding cochains) and a 1-parameter family of monotone Lagrangian tori $(S1\times S{n-1})_\tau$, with monotonicity constants $\tau>0$ (equipped with rank 1 unitary local systems). As a consequence, any closed orientable spin monotone Lagrangian (possibly equipped with auxiliary data) with non-trivial Floer cohomology is non-displaceable from either $Sn$ or one of the $(S1\times S{n-1})_\tau$. In the case of $T*S3$, the monotone Lagrangians $(S1\times S2)_\tau$ can be replaced by a family of monotone tori $T3_\tau$.

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