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From symplectic cohomology to Lagrangian enumerative geometry
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry. Univ Calif Berkeley, Berkeley, CA 94720 USA;HSE Univ, Moscow, Russia.
2019 (English)In: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 352, p. 717-776Article in journal (Refereed) Published
Abstract [en]

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. 

Place, publisher, year, edition, pages
ACADEMIC PRESS INC ELSEVIER SCIENCE , 2019. Vol. 352, p. 717-776
Keywords [en]
Mirror symmetry, Landau-Ginzburg potential, Lagrangian torus, Holomorphic disk, Symplectic cohomology, Enumerative geometry
National Category
Geometry
Identifiers
URN: urn:nbn:se:uu:diva-392127DOI: 10.1016/j.aim.2019.06.004ISI: 000477789300020OAI: oai:DiVA.org:uu-392127DiVA, id: diva2:1348197
Funder
Knut and Alice Wallenberg FoundationAvailable from: 2019-09-03 Created: 2019-09-03 Last updated: 2019-09-03Bibliographically approved

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