Lagrangian Intersection Floer Theory
Author | : Kenji Fukaya |
Publisher | : American Mathematical Society(RI) |
Total Pages | : 432 |
Release | : 2009 |
Genre | : Mathematics |
ISBN | : |
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Author | : Kenji Fukaya |
Publisher | : American Mathematical Society(RI) |
Total Pages | : 432 |
Release | : 2009 |
Genre | : Mathematics |
ISBN | : |
Author | : Yong-Geun Oh |
Publisher | : Springer Nature |
Total Pages | : 426 |
Release | : |
Genre | : |
ISBN | : 9819717981 |
Author | : Kenji Fukaya |
Publisher | : American Mathematical Soc. |
Total Pages | : 266 |
Release | : 2019-09-05 |
Genre | : Floer homology |
ISBN | : 1470436256 |
In this paper the authors first develop various enhancements of the theory of spectral invariants of Hamiltonian Floer homology and of Entov-Polterovich theory of spectral symplectic quasi-states and quasi-morphisms by incorporating bulk deformations, i.e., deformations by ambient cycles of symplectic manifolds, of the Floer homology and quantum cohomology. Essentially the same kind of construction is independently carried out by Usher in a slightly less general context. Then the authors explore various applications of these enhancements to the symplectic topology, especially new construction of symplectic quasi-states, quasi-morphisms and new Lagrangian intersection results on toric and non-toric manifolds. The most novel part of this paper is its use of open-closed Gromov-Witten-Floer theory and its variant involving closed orbits of periodic Hamiltonian system to connect spectral invariants (with bulk deformation), symplectic quasi-states, quasi-morphism to the Lagrangian Floer theory (with bulk deformation). The authors use this open-closed Gromov-Witten-Floer theory to produce new examples. Using the calculation of Lagrangian Floer cohomology with bulk, they produce examples of compact symplectic manifolds which admits uncountably many independent quasi-morphisms . They also obtain a new intersection result for the Lagrangian submanifold in .
Author | : Kenji Fukaya |
Publisher | : |
Total Pages | : 410 |
Release | : 2009 |
Genre | : Electronic books |
ISBN | : 9781470417482 |
This is a two-volume series research monograph on the general Lagrangian Floer theory and on the accompanying homological algebra of filtered A_\infty-algebras. This book provides the most important step towards a rigorous foundation of the Fukaya category in general context. In Volume I, general deformation theory of the Floer cohomology is developed in both algebraic and geometric contexts. An essentially self-contained homotopy theory of filtered A_\infty algebras and A_\infty bimodules and applications of their obstruction-deformation theory to the Lagrangian Floer theory are presented. Vo.
Author | : מאיר יהושואע יעקב קרופמן |
Publisher | : |
Total Pages | : |
Release | : 1904 |
Genre | : Bible |
ISBN | : |
Author | : Kenji Fukaya, Yong-Geun Oh, Hiroshi Ohta, Kaoru Ono |
Publisher | : American Mathematical Soc. |
Total Pages | : 410 |
Release | : |
Genre | : |
ISBN | : 082188848X |
Author | : Douglas Schultz |
Publisher | : |
Total Pages | : 126 |
Release | : 2017 |
Genre | : Symplectic manifolds |
ISBN | : |
Consider a fibration of compact symplectic manifolds F → E → B with a compatible symplectic form on E, and an induced fibration of Lagrangian submanifolds LF → L → LB. We develop a Leray-Serre type spectral sequence to compute the Floer cohomology of L in terms of the Floer complex of LF and LB when F is symplectically small. Moreover, we write down a formula for the leading order superpotential when F is a Kahler homogeneous space. To solve the transversality and compactness problem, we use the classical approach in addition to the perturbation scheme recently developed by Cieliebak-Mohnke [CM07] and Charest-Woodward [CWb; CWa]. As applications, we find Floer-non-trivial tori in complex flag manifolds and ruled surfaces.
Author | : Jack Edward Smith |
Publisher | : |
Total Pages | : |
Release | : 2017 |
Genre | : |
ISBN | : |
Author | : Société mathématique de France |
Publisher | : |
Total Pages | : 0 |
Release | : 2016 |
Genre | : |
ISBN | : |
Author | : |
Publisher | : |
Total Pages | : 0 |
Release | : 2016 |
Genre | : |
ISBN | : |
We adapt Lagrangian Floer theory on the de Rham complex developed by Fukaya [Fuk] and Fukaya-Oh-Ohta-Ono [FOOOToric2] and [FOOOToric3] for a Lagrangian torus fibration possibly with singular torus fibers under some assumptions, focusing on deformations of the Floer theory by degree 2 cycles from an ambient symplectic manifold. As an application, we detect non-displaceable torus fibers of a Lagrangian torus fibration with a singular fiber on Fano toric surfaces constructed by Auroux [Auroux1]. We detect a continuum of non-displaceable Lagrangian tori on some Fano toric surfaces that are not related to any standard toric fibers by any symplectomorphisms.