Lagrangian intersection floer theory : anomaly and obstruction
著者
書誌事項
Lagrangian intersection floer theory : anomaly and obstruction
（AMS/IP studies in advanced mathematics, v.46）
American Mathematical Society , International Press, 2009
- set
- pt. 1
- pt. 2
- pt. 1 : pbk
- pt. 2 : pbk
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pt. 1 : pbkS||AMSIP||46-1200021322058,
pt. 2 : pbkS||AMSIP||46-2200021322067 -
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注記
Includes bibliographical references and index
Other authors: Yong-Geun Oh, Hiroshi Ohta, Kaoru Ono
内容説明・目次
- 巻冊次
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set ISBN 9780821848319
内容説明
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. Volume II contains detailed studies of two of the main points of the foundation of the theory: transversality and orientation. The study of transversality is based on the virtual fundamental chain techniques (the theory of Kuranishi structures and their multisections) and chain level intersection theories. In this title, a detailed analysis comparing the orientations of the moduli spaces and their fiber products is carried out. A self-contained account of the general theory of Kuranishi structures is also included in the appendix of this volume.
目次
- Part I
- Introduction
- Review: Floer cohomology
- The $A_\infty$ algebra associated to a Lagrangian submanifold
- Homotopy equivalence of $A_\infty$ algebras
- Homotopy equivalence of $A_\infty$ bimodules
- Spectral sequences
- Part II
- Transversality
- Orientation
- Appendices
- Bibliography
- Index.
- 巻冊次
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pt. 1 : pbk ISBN 9780821852491
内容説明
A co-publication of the AMS and International Press of Boston, Inc.
This is a two-volume series research monograph on the general Lagrangian Floer theory and on the accompanying homological algebra of filtered A?A?-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?A? algebras and A?A? bimodules and applications of their obstruction-deformation theory to the Lagrangian Floer theory are presented. Volume II contains detailed studies of two of the main points of the foundation of the theory: transversality and orientation. The study of transversality is based on the virtual fundamental chain techniques (the theory of Kuranishi structures and their multisections) and chain level intersection theories. A detailed analysis comparing the orientations of the moduli spaces and their fiber products is carried out. A self-contained account of the general theory of Kuranishi structures is also included in the appendix of this volume.
- 巻冊次
-
pt. 2 : pbk ISBN 9780821852507
内容説明
A co-publication of the AMS and International Press of Boston, Inc.
This is a two-volume series research monograph on the general Lagrangian Floer theory and on the accompanying homological algebra of filtered A?A?-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?A? algebras and A?A? bimodules and applications of their obstruction-deformation theory to the Lagrangian Floer theory are presented. Volume II contains detailed studies of two of the main points of the foundation of the theory: transversality and orientation. The study of transversality is based on the virtual fundamental chain techniques (the theory of Kuranishi structures and their multisections) and chain level intersection theories. A detailed analysis comparing the orientations of the moduli spaces and their fiber products is carried out. A self-contained account of the general theory of Kuranishi structures is also included in the appendix of this volume.
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