Overview

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.

Full Product Details

Author:   Kenji Fukaya (Kyoto Univ, Japan) ,  Yong Geun Oh (Univ Of Wisconsin-madison, Usa & Korea Inst For Adv Study, South Korea) ,  K Ono (Hokkaido Univ, Japan) ,  Gang Tian (Massachusetts Inst Of Tech, Usa)
Publisher:   World Scientific Publishing Co Pte Ltd
Imprint:   World Scientific Publishing Co Pte Ltd
Dimensions:   Width: 15.70cm , Height: 3.00cm , Length: 23.00cm
Weight:   0.771kg
ISBN:  

9789810247140

ISBN 10:   9810247141
Pages:   508
Publication Date:   20 November 2001
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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