Lagrangian Intersection Floer Theory: Anomaly and Obstruction, Part I
Yong-Geun Oh, Hiroshi Ohta, and Kaoru Ono Kenji Fukaya
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.
Kategorien:
Band:
1 p.1
Jahr:
2009
Verlag:
American Mathematical Society
Sprache:
english
Seiten:
412
ISBN 10:
0821848364
ISBN 13:
9780821848364
Serien:
Ams/Ip Studies in Advanced Mathematics
Datei:
DJVU, 4.17 MB
IPFS:
,
english, 2009