نظریهٔ فلور تقاطع لاگرانژ: ناهنجاری و موانع، بخش دوم

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. Cover 1 Title 4 Contents 6 Preface 12 7 Transversality 14 8 Orientation 292 Appendices 370 Bibliography 408 Index 418 Back Cover 426 Kenji Fukaya ... [et Al.]. Includes Bibliographical References (p. 791-800) And Index.