From symplectic cohomology to Lagrangian enumerative geometry
Symplectic Geometry
2019-07-01 v3 Algebraic Geometry
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.
Keywords
Cite
@article{arxiv.1711.03292,
title = {From symplectic cohomology to Lagrangian enumerative geometry},
author = {Dmitry Tonkonog},
journal= {arXiv preprint arXiv:1711.03292},
year = {2019}
}
Comments
48 pages, 13 figures; v2: reference fixes, minor corrections; v3: minor changes, accepted version