Lagrangian Intersection Floer Theory : Anomaly and Obstruction, Part I Paperback / softback

A co-publication of the AMS and International Press of Boston, Inc. This is a two-volume series research monograph on the general Lagrangian Floer theory and on the accompanying homological algebra of filtered A?A?-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?A? algebras and A?A? 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.