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Lagrangian Intersection Floer Theory: Pt. 1: Anomaly and Obstruction (AMS/IP Studies in Advanced Mathematics) Book
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.Read More
from£125.09 | RRP: * Excludes Voucher Code Discount Also available Used from £N/A
- 0821848364
- 9780821848364
- Kenji Fukaya, Yong-Geun Oh, Hiroshi Ohta, Kaoru Ono
- 31 October 2009
- American Mathematical Society
- Hardcover (Book)
- 396
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