Year: 2018
Type: article
Abstract: In this paper we study Lagrangian Floer theory on toric manifolds from the point of view of mirror symmetry. We construct a natural isomorphism between the Frobenius manifold structures of the (big) quantum cohomology of the toric manifold and of Saito's theory of singularities of the potential function constructed in \cite{fooo09} via the Floer cohomology deformed by ambient cycles. Our proof of the isomorphism involves the open-closed Gromov-Witten theory of one-loop.
Source: Astérisque
DOI: 10.24033/ast.978
Authors: Kenji FUKAYA, Yong-Geun OH, Hiroshi OHTA, Kaoru ONO
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: Geometric moduli theory and its theoretical applications, Floer homology in mirror symmetry and in symplectic topology, G1808411863, Study on Floer theory and symplectic geometry, Proof of Homological Mirror Symmetry, G2583319762, Collaborative Research in Symplectic Topology, Pseudo-holomorphic map and Floer cohomology and their applications to symplectic geometry, G5012526392, Mirror symmetry conjecture and development of symplectic geometry, Floer theory, mirror symmetry conjecture and applications to symplectic geometry, Study on algebraic varieties related to moduli spaces and algebraic cycles, Studies on Floer thoery, theory of holomorphic curves and symplectic structures, contact structures, Development of Floer theory and study on symplectic structures
OpenAlex ID: W1524508048