Lagrangian Intersection Floer Theory Anomaly and Obstruction, Part I

Kenji Fukaya/ Yong-Geun Oh/ Hiroshi Ohta/ Kaoru Ono

ISBN 10: 0821852493 / ISBN 13: 9780821852491

Published by American Mathematical Society, 2010

About this Item

396 pages. 9.90x6.90x0.90 inches. In Stock.

Seller Inventory # __0821852493

Bibliographic Details

• Title: Lagrangian Intersection Floer Theory Anomaly and Obstruction, Part I
• Publisher: American Mathematical Society
• Publication Date: 2010
• Language: English
• ISBN 10: 0821852493
• ISBN 13: 9780821852491
• Binding: Paperback
• Condition: Brand New
• Weight: 0.71 kilograms

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