Softcover ISBN:  9780821852538 
Product Code:  AMSIP/46.S 
List Price:  $105.00 
MAA Member Price:  $94.50 
AMS Member Price:  $84.00 
Softcover ISBN:  9780821852538 
Product Code:  AMSIP/46.S 
List Price:  $105.00 
MAA Member Price:  $94.50 
AMS Member Price:  $84.00 

Book DetailsAMS/IP Studies in Advanced MathematicsVolume: 46; 2009; 800 ppMSC: Primary 53; Secondary 14; 81; 37; 18; 55;
This is a twovolume 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 selfcontained homotopy theory of filtered \(A_\infty\) algebras and \(A_\infty\) bimodules and applications of their obstructiondeformation 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 selfcontained account of the general theory of Kuranishi structures is also included in the appendix of this volume.
ReadershipGraduate students and research mathematicians interested in symplectic geometry, lowdimensional topology, mirror symmetry, and string theory.
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It should go without saying that this work is a major contribution to mathematics. ...the authors have done an admirable job in creating an approachable text, in which ideas are explained and constructions are sketched in a readable way first, with the full details available later if and when the reader is ready for them. The two volumes belong on the bookshelf of any modern symplectic topologist.
Mathematical Reviews


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This is a twovolume 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 selfcontained homotopy theory of filtered \(A_\infty\) algebras and \(A_\infty\) bimodules and applications of their obstructiondeformation 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 selfcontained account of the general theory of Kuranishi structures is also included in the appendix of this volume.
Graduate students and research mathematicians interested in symplectic geometry, lowdimensional topology, mirror symmetry, and string theory.

It should go without saying that this work is a major contribution to mathematics. ...the authors have done an admirable job in creating an approachable text, in which ideas are explained and constructions are sketched in a readable way first, with the full details available later if and when the reader is ready for them. The two volumes belong on the bookshelf of any modern symplectic topologist.
Mathematical Reviews