Floer homology in symplectic geometry and in mirror symmetry

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dc.creatorOh, Yong-Geun
dc.creatorFukaya, Kenji
dc.date2006-01-23
dc.date.accessioned2026-07-07T06:59:12Z
dc.date.available2026-07-07T06:59:12Z
dc.descriptionIn this article, the authors review what the Floer homology is and what it does in symplectic geometry both in the closed string and in the open string context. In the first case, the authors will explain how the chain level Floer theory leads to the $C^0$ symplectic invariants of Hamiltonian flows and to the study of topological Hamiltonian dynamics. In the second case, the authors explain how Floer's original construction of Lagrangian intersection Floer homology is obstructed in general as soon as one leaves the category of exact Lagrangian submanifolds. They will survey construction, obstruction and promotion of the Floer complex to the $A_\infty$ category of symplectic manifolds. Some applications of this general machinery to the study of the topology of Lagrangian embeddings in relation to symplectic topology and to mirror symmetry are also reviewed.
dc.descriptionTo appear in the Proceedings for ICM-2006 Madrid. This is the same version as the one submitted in December 2005 for the ICM proceedings, except the change of the style file due to the conflict of the ICM style file with the Archive posting
dc.identifierhttps://arxiv.org/abs/math/0601568
dc.identifierhttp://arxiv.org/abs/math/0601568
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/107666
dc.subjectSymplectic Geometry
dc.subjectAlgebraic Geometry
dc.subject53D40; 14J32
dc.titleFloer homology in symplectic geometry and in mirror symmetry
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