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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.
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
Linking options:
https://www.mathnet.ru/eng/rm9919https://doi.org/10.1070/RM9919 https://www.mathnet.ru/eng/rm/v75/i2/p133
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Abstract page: | 612 | Russian version PDF: | 115 | English version PDF: | 33 | References: | 68 | First page: | 46 |
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