Lectures on universal Teichm\"uller space

A. G. Sergeev

Lekcionnye kursy NOC, Lectures on universal Teichmüller space (2013), pp. 3-130.

Bibliographie

[1] A. G. Sergeev, Geometricheskoe kvantovanie prostranstv petel, Sovr. probl. matem., 13, MIAN, M., 2009, 294 pp. | DOI

[2] O. Lehto, Univalent Functions and Teichmüller Spaces, Grad. Texts in Math., 109, Springer-Verlag, Berlin, 1987 | MR | Zbl

[3] L. Alfors, Lektsii po kvazikonformnym otobrazheniyam, Mir, M., 1969 | MR | Zbl

[4] O. Lehto, K. I. Virtanen, Quasiconformal Mappings in the Plane, Grundlehren Math. Wiss., 126, Springer-Verlag, Berlin, 1973 | MR | Zbl

[5] S. Nag, The Complex Analytic Theory of Teichmüller Spaces, Canad. Math. Soc. Ser. Monogr. Adv. Texts, Wiley-Interscience Publ., New York, 1988 | MR | Zbl

[6] F. P. Gardiner, D. P. Sullivan, “Symmetric structures on a closed curve”, Amer. J. Math., 114:4 (1992), 683–736 | DOI | MR | Zbl

[7] A. Weil, “Sur les modules des surfaces de Riemann”, Sem. Bourbaki, 10 (1957)

[8] L. Ahlfors, “Curvature properties of Teichmüller's space”, J. Analyse Math., 9 (1961), 161–176

[9] R. Bowen, “Hausdorff dimension of quasicircles”, Inst. Hautes Études Sci. Publ. Math., 50 (1979), 11–25 | MR | Zbl

[10] A. A. Kirillov, D. V. Yurev, “Kelerova geometriya beskonechnomernogo odnorodnogo prostranstva $M=\operatorname{Diff}_+(S^1)/\operatorname{Rot}(S^1)$”, Funkts. analiz i ego pril., 21:4 (1987), 35–46 | MR | Zbl

[11] S. Nag, A. Verjovsky, “$\operatorname{Diff}(S^1)$ and the Teichmüller spaces”, Comm. Math. Phys., 130:1 (1990), 123–138 | DOI | MR | Zbl

[12] Kh. Tribel, Teoriya funktsionalnykh prostranstv, Mir, M., 1986 | MR | Zbl

[13] L. V. Ahlfors, Conformal Invariants. Topics in Geometric Function Theory, McGraw-Hill Ser. in Higher Math., McGraw Hill, New York, 1973 | MR | Zbl

[14] S. Nag, D. Sullivan, “Teichmüller theory and the universal period mapping via quantum calculus and the $H^{1/2}$ space on the circle”, Osaka J. Math., 32:1 (1995), 1–34 | MR | Zbl

[15] S. Nag, “A period mapping in universal Teichmüller space”, Bull. Amer. Math. Soc. (N.S.), 26:2 (1992), 280–287 | DOI | MR | Zbl

[16] D. Shale, “Linear symmetries of free boson field”, Trans. Amer. Math. Soc., 103 (1962), 149–167 | DOI | MR | Zbl

[17] F. A. Berezin, Metod vtorichnogo kvantovaniya, Nauka, M., 1986 | MR | Zbl

[18] G. Segal, “Unitary representations of some infinite dimensional groups”, Comm. Math. Phys., 80:3 (1981), 301–342 | DOI | MR | Zbl

[19] Sh. Kobayasi, K. Nomidzu, Osnovy differentsialnoi geometrii, T. 1, Nauka, M., 1981 | MR | Zbl

[20] R. Goodman, N. R. Wallach, “Structure and unitary cocycle representations of loop groups and the group of diffeomorphisms of the circle”, J. Reine Angew. Math., 347 (1984), 69–133 | MR | Zbl

[21] V. G. Kac, A. K. Raina, Bombay Lectures on Highest Weight Representations of Infinite-Dimensional Lie Algebras, Adv. Ser. Math. Phys., 2, World Sci., Singapore, 1987 | MR | Zbl

[22] S. C. Power, Hankel Operators on Hilbert Space, Res. Notes in Math., 64, Pitman, Boston, MA, 1982 | MR | Zbl

[23] J. Scherk, “An introduction to the theory of dual models and strings”, Rev. Mod. Phys., 47 (1975), 123–164 | DOI | MR | Zbl

[24] M. J. Bowick, S. G. Rajeev, “The holomorphic geometry of closed bosonic string theory and $\operatorname{Diff}S^1/S^1$”, Nuclear Phys. B, 293:2 (1987), 348–384 | DOI | MR

[25] L. A. Takhtajan, L.-P. Teo, Weil-Petersson Metric on the Universal Teichmüller Space, Mem. Amer. Math. Soc., 183, no. 861, Amer. Math. Soc., Providence, RI, 2006 | MR | Zbl

[26] H. M. Farkas, I. Kra, Riemann Surfaces, Grad. Texts in Math., 71, Springer-Verlag, Berlin, 1992 | MR | Zbl

[27] S. Wolpert, “The topology and geometry of the moduli space of Riemann surfaces”, Lecture Notes in Math., 1111, 1985, 431–451

[28] S. Wolpert, “On the Weil-Petersson geometry of the moduli space of curves”, Amer. J. Math., 107 (1985), 969–997

[29] S. Wolpert, “Chern forms and the Riemann tensor for the moduli space of curves”, Invent. Math., 85 (1986), 119–145

[30] P. G. Zograf, L. A. Takhtadzhyan, “Ob uravnenii Liuvillya, aktsessornykh parametrakh i geometrii prostranstva Teikhmyullera dlya rimanovykh poverkhnostei roda 0”, Matem. sb., 132:2 (1987), 147–166 | MR | Zbl

[31] P. G. Zograf, L. A. Takhtadzhyan, “Ob uniformizatsii rimanovykh poverkhnostei i metrike Veilya–Petersona na prostranstvakh Teikhmyullera i Shottki”, Matem. sb., 132:3 (1987), 304–321 | MR | Zbl

[32] E. Pressli, G. Sigal, Gruppy petel, Mir, M., 1990 | MR | Zbl

[33] N. M. J. Woodhouse, Geometric Quantization, Oxford Math. Monogr., Clarendon Press, Oxford, 1992 | MR | Zbl

[34] A. Connes, Géométrie Non Commutative, InterEditions, Paris, 1990 | MR | Zbl

[35] J. M. Gracia-Bondía, J. C. Várilly, H. Figueroa, Elements of Noncommutative Geometry, Birkhauser Adv. Texts Basler Lehrbucher, Birkhäuser Boston, Boston, MA, 2001 | MR | Zbl

[36] A. G. Sergeev, “The Group of Quasisymmetric Homeomorphisms of the Circle and Quantization of the Universal Teichmüller Space”, SIGMA, 5 (2009), 015, 20 pp. | DOI | MR | Zbl