Lagrangian Intersection Floer Theory: Anomaly and Obstruction

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

ISBN 10: 0821848372 / ISBN 13: 9780821848371

Published by American Mathematical Society(RI), 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: ...

Publisher: American Mathematical Society(RI)

Publication Date: 2009

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. In this title, 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.