Lagrangian Intersection Floer Theory
Author | : Kenji Fukaya |
Publisher | : American Mathematical Soc. |
Total Pages | : 426 |
Release | : 2010-06-21 |
ISBN-10 | : 9780821852507 |
ISBN-13 | : 0821852507 |
Rating | : 4/5 (507 Downloads) |
Download or read book Lagrangian Intersection Floer Theory written by Kenji Fukaya and published by American Mathematical Soc.. This book was released on 2010-06-21 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.