In search of infinite-dimensional K\"ahler geometry
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 75 (2020) no. 2, pp. 321-367
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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, half-differentiable strings.
Mots-clés : Dirac quantization
Mots-clés : Dirac quantization
@article{RM_2020_75_2_a2,
author = {A. G. Sergeev},
title = {In search of infinite-dimensional {K\"ahler} geometry},
journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
pages = {321--367},
publisher = {mathdoc},
volume = {75},
number = {2},
year = {2020},
language = {en},
url = {http://geodesic.mathdoc.fr/item/RM_2020_75_2_a2/}
}
A. G. Sergeev. In search of infinite-dimensional K\"ahler geometry. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 75 (2020) no. 2, pp. 321-367. http://geodesic.mathdoc.fr/item/RM_2020_75_2_a2/