In search of infinite-dimensional Kähler geometry

A. G. Sergeev

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 75 (2020) no. 2, pp. 321-367

Résumé

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.

Détail

Keywords: loop spaces of compact Lie groups, Hilbert–Schmidt Grassmannian manifolds, Virasoro algebra, half-differentiable strings.
Mots-clés : universal Teichmüller space, Dirac quantization

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