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Uspekhi Mat. Nauk, 2020, Volume 75, Issue 2(452), Pages 133–184 (Mi umn9919)  

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

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).


DOI: https://doi.org/10.4213/rm9919

Full text: PDF file (780 kB)
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References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 2020, 75:2, 321–367

Bibliographic databases:

UDC: 514.7+514.8
MSC: Primary 58B20; Secondary 22E67, 32G15, 32Q15, 81T30
Received: 04.10.2019

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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\pages 133--184
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\transl
\jour Russian Math. Surveys
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\pages 321--367
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  • https://doi.org/10.4213/rm9919
  • http://mi.mathnet.ru/eng/umn/v75/i2/p133

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. G. Sergeev, “Applications of noncommutative geometry in function theory and mathematical physics”, Trans. Moscow Math. Soc., 81:2 (2020), 123–167  mathnet  crossref  elib
  • Успехи математических наук Russian Mathematical Surveys
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