Author : Kenji Fukaya
Release : 2010-06-28
Genre : Mathematics
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Book Rating : 493/5 ( reviews)

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Lagrangian Intersection Floer Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lagrangian Intersection Floer Theory write by Kenji Fukaya. This book was released on 2010-06-28. Lagrangian Intersection Floer Theory available in PDF, EPUB and Kindle. 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.