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arXiv · 1711.03292

From symplectic cohomology to Lagrangian enumerative geometry

Dmitry Tonkonog
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Abstract

We build a bridge between Floer theory on open symplectic manifolds and the enumerative geometry of holomorphic disks inside their Fano compactifications, by detecting elements in symplectic cohomology which are mirror to Landau-Ginzburg potentials. We also treat the higher Maslov index versions of the potentials. We discover a relation between higher disk potentials and symplectic cohomology rings of smooth anticanonical divisor complements (themselves conjecturally related to closed-string Gromov-Witten invariants), and explore several other applications to the geometry of Liouville domains.

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Dmitry Tonkonog. 2017-11-09. From symplectic cohomology to Lagrangian enumerative geometry. https://doi.org/10.1016/j.aim.2019.06.004

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