Application de la théorie des déformations de Kodaira et Spencer à la mesure de Polyakov

Sarafopoulos, Georges

Publications du Département de mathématiques (Lyon), (1993), p. 1-66 / Harvested from Numdam

Détail

Publié le : 1993-01-01

Bibliographie

[1] Abraham, R-Marsden,J. Foundations of mechanics. New-York. Benjamin 1978. | MR 515141 | Zbl 0158.42901

[2] Ahlfors L. Some remarks on Teichmüller's space of Riemann surfaces. Annals of Maths. Vol.74 N°1 (1961). | MR 204641 | Zbl 0146.30602

[3] Atiyah M. The geometry and Physics of Knots Cambridge University Press 1990. | MR 1078014 | Zbl 0729.57002

[4] Belavin - Knizhnik. Complex geometry and the theory of Quantum Strings. Sov.Phys. J.E.T.P. 64 (2) August 1986. | MR 888370

[5] Berger, M-Ebin, D. Somme decompositions of the space of symetric tensors on a Riemann manifold. J. Diff. Geametry, 3, 379-392 (1969). | MR 266084 | Zbl 0194.53103

[6] Bismut J.M. - Bost J.B. Fibrés déterminants, métriques de Quillen et dégénerescence des courbes. C.R. Acad.Sci. t 307, Série I p.317-320 (1988). | MR 958789 | Zbl 0652.32019

[7] Bismut J.M. - Gillet H. - Soule G. Soule G. Analytic Torsion and Holomorphic Déterminant Bundles. I. Bott-Chem Forms and Analytic Torsion Commun. Math.Phys. 115, p.49-78 (1988) | MR 929146 | Zbl 0651.32017

Bismut J.M. - Gillet H. - Soule G. Analytic Torsion and Holomorphic Déterminant Bundles II. Direct Images and Bott-Chem Forms Commun. Math. Phys. 115, p.79-126 (1988). | MR 929147 | Zbl 0651.32017

Bismut J.M. - Gillet H. - Soule G. Analytic Torsion and Holomorphic Déterminant Bundles III. Analytic Torsion and Holomorphic Determinant Bundles. Commun.Math.Phys. 115, 301-351 (1988). | MR 931666 | Zbl 0651.32017

[8] Bost J.B. Fibrés déterminants, déterminants régularisés et mesures sur les espaces de modules des courbes complexes. Sém.Bourbaki n°676 - Février 1987. | Numdam | Zbl 0655.32021

[9] Bost J.B. - Jolic_Ur A holomorphic property and the critical dimension in string theory from an index theorem. Phys.Lett. B 174 (1986) p.273-276. | MR 848539

[10] D'Hoker - Phong Multiloop amplitudes for the bosonic Polyakov string. Nucl. Phys. B.269 (1986) p.205-234. | MR 838673

[11] Fischer A.E. - Tromba A.J. : On a Purely Riemannian Proof of the structure and dimension of the Unramified Moduli Space of a Compact Riemann Surface Math. An. 267, 311-345 (1984). | MR 738256 | Zbl 0518.32015

[12] Fischer A.E. - Tromba A.J. Almost complex principal fiber bundles and the complex structure on Teichmüller Space. Crelles J. Band. 352, 151-160 (1984). | MR 758699 | Zbl 0573.32021

[13] Fischer A.E. - Tromba A.J. On the Weil-Pelersson metric on Teichmüller Space. Trans. A.M.S. 284, 319-335 (1984). | MR 742427 | Zbl 0578.58006

[14] Freed D. Determinants, Torsion and Strings. Commun. Math.Phys. 107, 483-533 (1986). | MR 866202 | Zbl 0606.58013

[15] Gilkey P.B. Invariance theory, the heat equation and the Atiyah-Singer index theorem. Puplish or Perish, 1984. | MR 783634 | Zbl 0565.58035

[16] Kobayashi, S-Nomizu, K Foundations of differential geometry. New-York : Intersciences 1963. | MR 152974 | Zbl 0175.48504

[17] Kodaira K - Spencer D. G. On deformations of complex structures I, II, III. An of Math. Vol.67, (1958). | MR 112154 | Zbl 0128.16901

Kodaira K - Spencer D. G. On deformations of complex structures I, II, III. An of Math. Vol.71 (1960) | MR 115189 | Zbl 0128.16902

[18] Kodaira K - Nirenberg L. - Spencer D.G. On the existence of deformations of complex analytic structures. An. of Math. Vol.68 (1958). | MR 112157 | Zbl 0088.38004

[19] Lang S. An introduction to Arakelov theory Springer-Verlag 1988. | MR 969124 | Zbl 0667.14001

[20] Lehto O. Univalent Functions and Teichmüller Spaces G.T.M. Springer-Verlag 1987. | MR 867407 | Zbl 0606.30001

[21] Mumford D. Stability of projective varieties. L'Enseignement Mathématique 23 (1977). | MR 450273 | Zbl 0363.14003

[22] Mumford D - Knudsen F. The projectivity of the moduli space of stable curves. I. - Preliminaries on "det" and "div" Math. Scand. 39 (1976). | MR 437541 | Zbl 0343.14008

[23] Nag S. The complex analytic theory of Teichmüller spaces. Canadian Math. Society Series of monographies and advanced texts. John-Wiley 1988. | MR 927291 | Zbl 0667.30040

[24] Newlander, A. - Nirenberg, L. Complex analytic coodinates in almost-complex manifolds. Annals of Maths. 65 (1957). | MR 88770 | Zbl 0079.16102

[25] Omori, H. On the group of diffeomorphism on a compact manifold. Proc.Sym.Pure Math.AMS 15 (1970). | MR 271983 | Zbl 0214.48805

[26] Palais, R. Foundations of global non-linear analysis. New-York. Benjamin 1968. | MR 248880 | Zbl 0164.11102

[27] Polyakov A.M. Quantum geometry of bosonic strings Phys. lett. 103 B 207-210 (1981). | MR 623209

[28] Powell, J. Two theorems on the mapping class group of a surface. Proc. AMS 68 (1978). | MR 494115 | Zbl 0391.57009

[29] Quillen D. Determinant of Cauchy-Riemann operators over a Riemann surface. Funct. Anal.Appl. 19 (1985). | MR 783704 | Zbl 0603.32016

[30] Ray D. - Singer I.M. R-torsion and the laplacian on riemann manifolds Adv. in Math. 7, 145-210 (1971). | MR 295381 | Zbl 0239.58014

[31] Seeley R.T. Complex powers of an elliptic operator. Proc. Symp.Pure Math. AMS Vol.X (1967). | MR 237943 | Zbl 0159.15504

[32] Singer I.M. Some Problems in the Quantization of Gauge theories and String theories. Proce.Symp.Pure Math. Vol.48 (1988). | MR 974336 | Zbl 0702.58010

[33] Takhtajan L.A. Uniformization, local Index theorem and geometry of the moduli Spaces of Riemann surfaces and vector Bundles. Proc.Symp.Pure Math. Vol.49 (1989) Part.I. | MR 1013154 | Zbl 0689.30035

[34] Tomi F - Tromba A.J. Existence theorems for minimal surfaces of non-zero genus spanning a contour. Memoirs A.M.S. Vol.71 N°382 (1988). | MR 920962 | Zbl 0638.58004

[35] Wells Differential Analysis on Complex manifolds. Prendice-Hall Series in modem analysis 1973. | MR 515872 | Zbl 0435.32004