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Symplectic Geometry And Mirror Symmetry - Proceedings Of The 4th Kias Annual International Conference - Kenji Fukaya

Symplectic Geometry And Mirror Symmetry - Proceedings Of The 4th Kias Annual International Conference

By: Kenji Fukaya (Editor), Yong-Geun Oh (Editor), Gang Tian (Editor)


Published: 19th November 2001
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In 1993, M. Kontsevich proposed a conceptual framework for explaining the phenomenon of mirror symmetry. Mirror symmetry had been discovered by physicists in string theory as a duality between families of three-dimensional Calabi-Yau manifolds. Kontsevich's proposal uses Fukaya's construction of the A-psi-category of Lagrangian submanifolds on the symplectic side and the derived category of coherent sheaves on the complex side. The theory of mirror symmetry was further enhanced by physicists in the language of D-branes and also by Strominger-Yau-Zaslow in the geometric set-up of (special) Lagrangian torus fibrations. It rapidly expanded its scope across from geometry, topology, algebra to physics. In this volume, leading experts in the field explore recent developments in relation to homological mirror symmetry, Floer theory, D-branes and Gromov-Witten invariants. Kontsevich-Soibelman describe their solution to the mirror conjecture on the abelian variety based on the deformation theory of A-psi-categories, and Ohta describes recent work on the Lagrangian intersection Floer theory by Fukaya-Oh-Ohta-Ono which takes an important step towards a rigorous construction of the A-psi-category. There follow a number of contributions on the homological mirror symmetry, D-branes and the Gromov-Witten invariants: for example, Getzler shows how the Toda conjecture follows from recent work of Givental, Okounkov and Pandharipande. This volume provides a presentation of the important developments of recent years in this rapidly growing field.

Estimated transversality in symplectic geometry and projective mapsp. 1
Local mirror symmetry and five-dimensional gauge theoryp. 31
The Toda conjecturep. 51
Examples of special Lagrangian fibrationsp. 81
Linear models of supersymmetric D-branesp. 111
The connectedness of the moduli space of maps to homogeneous spacesp. 187
Homological mirror symmetry and torus fibrationsp. 203
Genus-1 Virasoro conjecture on the small phase spacep. 265
Obstruction to and deformation of Lagrangian intersection Floer cohomologyp. 281
Topological open p-branesp. 311
Lagrangian torus fibration and mirror symmetry of Calabi-Yau manifoldsp. 385
More about vanishing cycles and mutationp. 429
Moment maps, monodromy and mirror manifoldsp. 467
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9789810247140
ISBN-10: 9810247141
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 498
Published: 19th November 2001
Country of Publication: SG
Dimensions (cm): 21.84 x 15.75  x 3.05
Weight (kg): 0.77