Spectral invariants with bulk, quasi-morphisms and Lagrangian Floer theory /
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| Author / Creator: | Fukaya, Kenji, 1959- author. |
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| Imprint: | Providence, RI : American Mathematical Society, 2019. ©2019 |
| Description: | x, 266 pages : illustrations ; 26 cm. |
| Language: | English |
| Series: | Memoirs of the American Mathematical Society 1947-6221 volume 260, number 1254 Memoirs of the American Mathematical Society ; no. 1254. |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/11948552 |
| Summary: | 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.<br> <br> 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).<br> <br> 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 $(M,\omega)$ which admits uncountably many independent quasi-morphisms $\widetilde{{{{\rm Ham}}}}(M,\omega) \to {{\mathbb{{R}}}}$. They also obtain a new intersection result for the Lagrangian submanifold in $S^2 \times S^2$. |
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| Item Description: | "July 2019, Volume 260, Number 1254 (third of 5 numbers)." |
| Physical Description: | x, 266 pages : illustrations ; 26 cm. |
| Bibliography: | Includes bibliographical references (pages 257-261) and index. |
| ISBN: | 1470436256 9781470436254 |
| ISSN: | 1947-6221 |