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

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

Hardcover

ISBN 10: 0821848372 ISBN 13: 9780821848371

Publisher: American Mathematical Society, 2009

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.

Edition details

• Publisher: American Mathematical Society
• Publication date: 2009
• ISBN 10: 0821848372
• ISBN 13: 9780821848371
• Binding: Hardcover
• Language: English
• Edition number: 1
• Number of pages: 404