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dc.contributor.authorChan, Kwokwaien_US
dc.contributor.authorLau, Siu-Cheongen_US
dc.contributor.authorLeung, Naichung Conanen_US
dc.contributor.authorTseng, Hsian-Huaen_US
dc.date.accessioned2018-10-26T15:02:33Z
dc.date.available2018-10-26T15:02:33Z
dc.date.issued2017-06
dc.identifier.citationKwokwai Chan, Siu-Cheong Lau, Naichung Conan Leung, Hsian-Hua Tseng. 2017. "Open Gromov–Witten invariants, mirror maps, and Seidel representations for toric manifolds." Duke Mathematical Journal, v. 166, Issue 8, pp. 1405 - 1462. https://doi.org/10.1215/00127094-0000003X
dc.identifier.issn0012-7094
dc.identifier.urihttps://hdl.handle.net/2144/31669
dc.description.abstractLet X be a compact toric Kähler manifold with −KX nef. Let L⊂X be a regular fiber of the moment map of the Hamiltonian torus action on X. Fukaya, Oh, Ohta, and Ono defined open Gromov–Witten (GW) invariants of X as virtual counts of holomorphic disks with Lagrangian boundary condition L. We prove a formula that equates such open GW invariants with closed GW invariants of certain X-bundles over ℙ1 used by Seidel and McDuff earlier to construct Seidel representations for X. We apply this formula and degeneration techniques to explicitly calculate all these open GW invariants. This yields a formula for the disk potential of X, an enumerative meaning of mirror maps, and a description of the inverse of the ring isomorphism of Fukaya, Oh, Ohta, and Ono.en_US
dc.format.extentp. 1405-1462en_US
dc.relation.ispartofDuke Mathematical Journal
dc.relation.isversionof10.1215/00127094-0000003X
dc.subjectPure mathematicsen_US
dc.subjectGeneral mathematicsen_US
dc.titleOpen Gromov–Witten invariants, mirror maps, and Seidel representations for toric manifoldsen_US
dc.typeArticleen_US
dc.identifier.doi10.1215/00127094-0000003X
pubs.elements-sourcecrossrefen_US
pubs.notesEmbargo: Not knownen_US
pubs.organisational-groupBoston Universityen_US
pubs.organisational-groupBoston University, College of Arts & Sciencesen_US
pubs.organisational-groupBoston University, College of Arts & Sciences, Department of Mathematics & Statisticsen_US
pubs.publication-statusPublisheden_US


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