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Russian Mathematical Surveys, 2004, Volume 59, Issue 5, Pages 907–940
DOI: https://doi.org/10.1070/RM2004v059n05ABEH000772
(Mi rm772)
 

This article is cited in 13 scientific papers (total in 13 papers)

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

A. N. Kapustina, D. O. Orlovb

a California Institute of Technology
b Steklov Mathematical Institute, Russian Academy of Sciences
References:
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”.
Received: 05.08.2004
Bibliographic databases:
Document Type: Article
UDC: 512.7+514.7
MSC: Primary 14J32, 18E30; Secondary 14F05, 53D12, 57R58, 81T30, 32Q25, 81T45, 57R56
Language: English
Original paper language: Russian
Citation: A. N. Kapustin, D. O. Orlov, “Lectures on mirror symmetry, derived categories, and $D$-branes”, Russian Math. Surveys, 59:5 (2004), 907–940
Citation in format AMSBIB
\Bibitem{KapOrl04}
\by A.~N.~Kapustin, D.~O.~Orlov
\paper Lectures on mirror symmetry, derived categories, and $D$-branes
\jour Russian Math. Surveys
\yr 2004
\vol 59
\issue 5
\pages 907--940
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\crossref{https://doi.org/10.1070/RM2004v059n05ABEH000772}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2125928}
\zmath{https://zbmath.org/?q=an:1074.14036}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2004RuMaS..59..907K}
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\elib{https://elibrary.ru/item.asp?id=13445867}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-14544308714}
Linking options:
  • https://www.mathnet.ru/eng/rm772
  • https://doi.org/10.1070/RM2004v059n05ABEH000772
  • https://www.mathnet.ru/eng/rm/v59/i5/p101
  • This publication is cited in the following 13 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Успехи математических наук Russian Mathematical Surveys
    Statistics & downloads:
    Abstract page:1566
    Russian version PDF:917
    English version PDF:56
    References:103
    First page:4
     
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