Kontsevich, M. L. Virasoro algebra and Teichmüller spaces. (English. Russian original) Zbl 0647.58012 Funct. Anal. Appl. 21, No. 1-3, 156-157 (1987); translation from Funkts. Anal. Prilozh. 21, No. 2, 78-79 (1987). It is shown that the set of equivalence classes of triples \((C,p,t)\), where \(C\) is a complex Riemann surface of genus \(g\), \(p\) a point of \(C\) and \(t\) an \(\infty\)-jet of a coordinate at \(p\) is infinitesimally a double coset space of the central extension of the group of diffeomorphisms of the circle (the Virasoro group) modulo analogues of a compact and a discrete subgroup and its embedding into an infinite dimensional Grassmannian is described. Fortunately, these results, discovered independently, are presented in more detailed and easier to read form in A. A. Beilinson and V. V. Schechtman [Commun. Math. Phys. 118, 651–701 (1988; Zbl 0665.17010)], B. Arbarello, C. De Concini, V. Kac and C. Procesi, Commun. Math. Phys. 117, No. 1, 1–36 (1988; Zbl 0647.17010)] and [N. Kawamoto, Y. Namikawa, A. Tsuchiya and Y. Yamada, Commun. Math. Phys. 116, No. 2, 247–308 (1988; Zbl 0648.35080)]. Reviewer: D.A.Leites Cited in 1 ReviewCited in 18 Documents MSC: 58D05 Groups of diffeomorphisms and homeomorphisms as manifolds 58B20 Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds 17B68 Virasoro and related algebras 22E65 Infinite-dimensional Lie groups and their Lie algebras: general properties Keywords:Teichmüller spaces; Virasoro algebra; Virasoro group Citations:Zbl 0647.17010; Zbl 0665.17010; Zbl 0648.35080 PDFBibTeX XMLCite \textit{M. L. Kontsevich}, Funct. Anal. Appl. 21, No. 1--3, 156--157 (1987; Zbl 0647.58012); translation from Funkts. Anal. Prilozh. 21, No. 2, 78--79 (1987) Full Text: DOI References: [1] Yu. I. Manin, Funkts. Anal. Prilozhen.,20, No. 3, 88-89 (1986). [2] I. V. Cherednik, Funkts. Anal. Prilozhen.,19, No. 3, 36-52 (1985). [3] D. Mumford, L’Enseign Math., Ser. 2,23, No. 1-2, 39-110 (1977). This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.