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Lectures on mirror symmetry, derived categories, and D-branes

Kapustin, Anton and Orlov, Dmitri (2004) Lectures on mirror symmetry, derived categories, and D-branes. Russian Mathematical Surveys, 59 (5). pp. 907-940. ISSN 0036-0279. https://resolver.caltech.edu/CaltechAUTHORS:20160506-151404465

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Abstract

This paper, mainly intended for a mathematical audience, is an introduction to homological mirror symmetry, derived categories, and topological D-branes. Mirror symmetry from the point of view of physics is explained, along with the relationship between symmetry and derived categories, and the reason why the Fukaya category must be extended by using co-isotropic A-branes. There is also a discussion of how to extend the definition of the Floer homology to these objects and a description of mirror symmetry for flat tori. The paper consists of four lectures given at the Institute of Pure and Applied Mathematics (Los Angeles) in March 2003, as a part of the programme “Symplectic Geometry and Physics”.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1070/RM2004v059n05ABEH000772DOIArticle
http://www.turpion.org/php/paper.phtml?journal_id=rm&paper_id=772PublisherArticle
http://arxiv.org/abs/math/0308173v2arXivDiscussion Paper
ORCID:
AuthorORCID
Kapustin, Anton0000-0003-3903-5158
Orlov, Dmitri0000-0002-2230-457X
Additional Information:© 2004 Turpion Ltd. The first author was supported in part by the DOE grant DE-FG03-92-ER40701. The second author was supported in part by the grant of the President of RF for young scientists D-2731.2004.1, by Civic Research Development Foundation (CRDF Award No RM1-2405-MO-02), and by the Russian Science Support Foundation.
Funders:
Funding AgencyGrant Number
Department of Energy (DOE)DE-FG03-92-ER40701
President of of the Russian FederationD-2731.2004.1
Civilian Research and Development Foundation for the Independent States of the Former Soviet Union (CRDF)RM1-2405-MO-02
Russian Science Support FoundationUNSPECIFIED
Issue or Number:5
Classification Code:AMS MSC: Primary: 14J32, 18E30, Secondary: 14F05, 53D12, 57R58, 81T30, 32Q25, 81T45, 57R56
Record Number:CaltechAUTHORS:20160506-151404465
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20160506-151404465
Official Citation:A N Kapustin, D O Orlov, "Lectures on mirror symmetry, derived categories, and D-branes", RUSS MATH SURV, 2004, 59 (5), 907–940
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:66717
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:06 May 2016 23:19
Last Modified:03 Oct 2019 09:59

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