Lagrangian Floer Theory and Mirror Symmetry on Compact Toric Manifolds
Lagrangian Floer Theory and Mirror Symmetry on Compact Toric Manifolds (Asterisque) by Kenji Fukaya and Yong-geun Oh
English | 2016 | ISBN: 2856298257 | 340 pages | PDF | 3 MB
English | 2016 | ISBN: 2856298257 | 340 pages | PDF | 3 MB
In this volume 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 [Fukaya, Tohoku Math. J. 63 (2011)] via the Floer cohomology deformed by ambient cycles. Our proof of the isomorphism involves the open-closed Gromov-Witten theory of one-loop.