Author : Kenji Fukaya
Release : 2019-09-05
Genre : Floer homology
Kind :
Book Rating : 256/5 ( reviews)

GET EBOOK

Spectral Invariants with Bulk, Quasi-Morphisms and Lagrangian Floer Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Spectral Invariants with Bulk, Quasi-Morphisms and Lagrangian Floer Theory write by Kenji Fukaya. This book was released on 2019-09-05. Spectral Invariants with Bulk, Quasi-Morphisms and Lagrangian Floer Theory available in PDF, EPUB and Kindle. 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 .