Lagrangian Intersection Floer Theory: Anomaly and Obstruction, Part II (AMS/IP Studies in Advanced Mathematics, Vol. 46)

Kenji Fukaya, Yong-Geun Oh, Hiroshi Ohta, and Kaoru Ono

ISBN 10: 0821848372 / ISBN 13: 9780821848371

Published by American Mathematical Society, 2009

About this Item

Former library book; Pages can have notes/highlighting. Spine may show signs of wear. ~ ThriftBooks: Read More, Spend Less 1.01.

Seller Inventory # G0821848372I3N10

Bibliographic Details

• Title: Lagrangian Intersection Floer Theory: Anomaly and Obstruction, Part II (AMS/IP Studies in Advanced Mathematics, Vol. 46)
• Publisher: American Mathematical Society
• Publication Date: 2009
• Language: English
• ISBN 10: 0821848372
• ISBN 13: 9780821848371
• Binding: Hardcover
• Condition: Good
• Dust Jacket Condition: No Jacket

About this title

Synopsis

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.