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Russian Mathematical Surveys, 2020, Volume 75, Issue 2, Pages 321–367
DOI: https://doi.org/10.1070/RM9919 (Mi rm9919) 		 
This article is cited in 1 scientific paper (total in 1 paper)

In search of infinite-dimensional Kähler geometry

A. G. Sergeev

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
English version PDF (760 kB) Citations (1)
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DOI: https://doi.org/10.1070/RM9919
Abstract: This paper is devoted to a survey of recent results in the Kähler geometry of infinite-dimensional Kähler manifolds. Three particular classes of such manifolds are investigated: the loop spaces of compact Lie groups, Hilbert–Schmidt Grassmannians, and the universal Teichmüller space. These investigations have been prompted both by requirements in Kähler geometry itself and by connections with string theory, which are considered in the last section.
Bibliography: 43 titles.
Keywords: loop spaces of compact Lie groups, Hilbert–Schmidt Grassmannian manifolds, universal Teichmüller space, Virasoro algebra, Dirac quantization, half-differentiable strings.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-15-2019-1614
This work was performed at the Steklov International Mathematical Centre and supported by the Ministry of Science and Higher Education of the Russian Federation (agreement no. 075-15-2019-1614).
Received: 04.10.2019
Russian version:
Uspekhi Matematicheskikh Nauk, 2020, Volume 75, Issue 2(452), Pages 133–184
DOI: https://doi.org/10.4213/rm9919
Bibliographic databases:
Document Type: Article
UDC: 514.7+514.8
MSC: Primary 58B20; Secondary 22E67, 32G15, 32Q15, 81T30
Language: English
Original paper language: Russian
Citation: A. G. Sergeev, “In search of infinite-dimensional Kähler geometry”, Uspekhi Mat. Nauk, 75:2(452) (2020), 133–184; Russian Math. Surveys, 75:2 (2020), 321–367
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
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    Abstract page:618
    Russian version PDF:115
    English version PDF:33
    References:68
    First page:46
     
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