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Lagrangian Intersection Floer Theory: Anomaly and Obstruction, Part I
 
Kenji Fukaya Kyoto University, Kyoto, Japan
Yong-Geun Oh University of Wisconsin, Madison, Madison, WI
Hiroshi Ohta Nagoya University, Nagoya, Japan
Kaoru Ono Hokkaido University, Sapporo, Japan
A co-publication of the AMS and International Press of Boston
Lagrangian Intersection Floer Theory
Softcover ISBN:  978-0-8218-5249-1
Product Code:  AMSIP/46.1.S
List Price: $59.00
MAA Member Price: $53.10
AMS Member Price: $47.20
eBook ISBN:  978-1-4704-1748-2
Product Code:  AMSIP/46.1.E
List Price: $55.00
MAA Member Price: $49.50
AMS Member Price: $44.00
Softcover ISBN:  978-0-8218-5249-1
eBook: ISBN:  978-1-4704-1748-2
Product Code:  AMSIP/46.1.S.B
List Price: $114.00 $86.50
MAA Member Price: $102.60 $77.85
AMS Member Price: $91.20 $69.20
Lagrangian Intersection Floer Theory
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Lagrangian Intersection Floer Theory: Anomaly and Obstruction, Part I
Kenji Fukaya Kyoto University, Kyoto, Japan
Yong-Geun Oh University of Wisconsin, Madison, Madison, WI
Hiroshi Ohta Nagoya University, Nagoya, Japan
Kaoru Ono Hokkaido University, Sapporo, Japan
A co-publication of the AMS and International Press of Boston
Softcover ISBN:  978-0-8218-5249-1
Product Code:  AMSIP/46.1.S
List Price: $59.00
MAA Member Price: $53.10
AMS Member Price: $47.20
eBook ISBN:  978-1-4704-1748-2
Product Code:  AMSIP/46.1.E
List Price: $55.00
MAA Member Price: $49.50
AMS Member Price: $44.00
Softcover ISBN:  978-0-8218-5249-1
eBook ISBN:  978-1-4704-1748-2
Product Code:  AMSIP/46.1.S.B
List Price: $114.00 $86.50
MAA Member Price: $102.60 $77.85
AMS Member Price: $91.20 $69.20
  • Book Details
     
     
    AMS/IP Studies in Advanced Mathematics
    Volume: 462009; 396 pp
    MSC: Primary 53; Secondary 14; 81; 37; 18; 55

    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. 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.

    Titles in this series are co-published with International Press of Boston, Inc., Cambridge, MA.

    Readership

    Graduate students and research mathematicians interested in symplectic geometry, low-dimensional topology, mirror symmetry, and string theory.

    This item is also available as part of a set:
  • Table of Contents
     
     
    • Chapters
    • Chapter 1. Introduction
    • Chapter 2. Review: Floer cohomology
    • Chapter 3. The $A_\infty $ algebra associated to a Lagrangian submanifold
    • Chapter 4. Homotopy equivalence of $A_\infty $ algebras
    • Chapter 5. Homotopy equivalence of $A_\infty $ bimodules
    • Chapter 6. Spectral sequences
  • Additional Material
     
     
  • Reviews
     
     
    • It should go without saying that this work is a major contribution to mathematics. ...the authors have done an admirable job in creating an approachable text, in which ideas are explained and constructions are sketched in a readable way first, with the full details available later if and when the reader is ready for them. The two volumes belong on the bookshelf of any modern symplectic topologist.

      Mathematical Reviews
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 462009; 396 pp
MSC: Primary 53; Secondary 14; 81; 37; 18; 55

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. 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.

Titles in this series are co-published with International Press of Boston, Inc., Cambridge, MA.

Readership

Graduate students and research mathematicians interested in symplectic geometry, low-dimensional topology, mirror symmetry, and string theory.

This item is also available as part of a set:
  • Chapters
  • Chapter 1. Introduction
  • Chapter 2. Review: Floer cohomology
  • Chapter 3. The $A_\infty $ algebra associated to a Lagrangian submanifold
  • Chapter 4. Homotopy equivalence of $A_\infty $ algebras
  • Chapter 5. Homotopy equivalence of $A_\infty $ bimodules
  • Chapter 6. Spectral sequences
  • It should go without saying that this work is a major contribution to mathematics. ...the authors have done an admirable job in creating an approachable text, in which ideas are explained and constructions are sketched in a readable way first, with the full details available later if and when the reader is ready for them. The two volumes belong on the bookshelf of any modern symplectic topologist.

    Mathematical Reviews
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
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