**AMS/IP Studies in Advanced Mathematics**

Volume: 46;
2009;
800 pp;
Softcover

MSC: Primary 53;
Secondary 14; 81; 37; 18; 55

**Print ISBN: 978-0-8218-5253-8
Product Code: AMSIP/46.S**

List Price: $94.00

AMS Member Price: $75.20

MAA Member Price: $84.60

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#### Supplemental Materials

# Lagrangian Intersection Floer Theory: Anomaly and Obstruction

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*Kenji Fukaya; Yong-Geun Oh; Hiroshi Ohta; Kaoru Ono*

A co-publication of the AMS and International Press of Boston

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.

#### Reviews & Endorsements

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