Formes de torsion analytique et familles des submersions I
Bulletin de la Société Mathématique de France, Tome 127 (1999) no. 4, pp. 541-621.
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Xiaonan, Ma. Formes de torsion analytique et familles des submersions I. Bulletin de la Société Mathématique de France, Tome 127 (1999) no. 4, pp. 541-621. doi : 10.24033/bsmf.2360. http://www.numdam.org/articles/10.24033/bsmf.2360/

[ABoP] Atiyah (M.F.), Bott (R.), Patodi. (V.K.). - On the heat equation and the Index Theorem, Invent. Math., t. 19, 1973, p. 279-330. | MR | Zbl

[BaFM] Baum (P.), Fulton (W.), Macpherson (R.). - Riemann-Roch for singular varietes, Publ. Math. IHES, t. 45, 1975, p. 101-146. | Numdam | MR | Zbl

[BeGeV] Berline (N.), Getzler (E.), Vergne (M.). - Heat kernels and the Dirac operator. - Grundl. Math. Wiss., 298, Springer, Berlin-Heidelberg-New York, 1992. | MR | Zbl

[BerB] Berthomieu (A.), Bismut (J.-M.). - Quillen metric and higher analytic torsion forms, J. Reine angew. Math., t. 457, 1994, p. 85-184. | MR | Zbl

[B1] Bismut (J.-M.). - The Index Theorem for families of Dirac operators : two heat equation proofs, Invent. Math., t. 83, 1986, p. 91-151. | MR | Zbl

[B3] Bismut (J.-M.). - Koszul complexes, harmonic oscillators and the Todd class, J. Amer. Math. Soc., t. 3, 1990, p. 159-256. | MR | Zbl

[B4] Bismut (J.-M.). - Families of immersions, and higher analytic torsion, Astérisque, 244, 1997. | Numdam | MR | Zbl

[B5] Bismut (J.-M.). - Familles d'immersions et formes de torsion analytique en degré supérieur, C.R.A.S. Paris, t. 320, série I, 1995, p. 969-974. | MR | Zbl

[BCh] Bismut (J.-M.), Cheeger (J.). - η-invariants and their adiabatic limits, J. Amer. Math. Soc., t. 2, 1989, p. 33-70. | MR | Zbl

[BGS1] Bismut (J.-M.), Gillet (H.), Soulé (C.). - Analytic torsion and holomorphic determinant bundles I, Comm. Math. Phys., t. 115, 1988, p. 49-78. | MR | Zbl

[BGS2] Bismut (J.-M.), Gillet (H.), Soulé (C.). - Analytic torsion and holomorphic determinant bundles II, Comm. Math. Phys., t. 115, 1988, p. 79-126. | MR | Zbl

[BGS3] Bismut (J.-M.), Gillet (H.), Soulé (C.). - Analytic torsion and holomorphic determinant bundles III, Comm. Math. Phys., t. 115, 1988, p. 301-351. | MR | Zbl

[BKö] Bismut (J.-M.), Köhler (K.). - Higher analytic torsion forms for direct images and anomaly formulas, J. Alg. Geom., t. 1, 1992, p. 647-684. | MR | Zbl

[BL] Bismut (J.-M.), Lebeau (G.). - Complex immersions and Quillen metrics, Publ. Math. IHES, 74, 1991, p. 1-297. | Numdam | MR | Zbl

[BS] Borel (A.), Serre (J.-P.). - Le théorème de Riemann-Roch, Bull. Soc. Math. France, t. 86, 1958, p. 97-136. | Numdam | MR | Zbl

[CE] Cartan (H.), Eilenberg (S.). - Homological Algebra. - Princeton, 1956. | MR | Zbl

[CP] Charazain (J.), Piriou (A.). - Introduction à la théorie des équations aux dérivées partielles. - Gauthier-Villars, Paris, 1981. | Zbl

[D] Dai (X.). - Adiabatic limits, non multiplicativity of signature and Leray spectal sequence, J. Amer. Math. Soc., t. 4, 1991, p. 265-321. | MR | Zbl

[F] Faltings (G.). - Lectures on the arithmetic Riemann-Roch Theorem, Ann. Math. Studies, Princeton University Press, 1992. | MR | Zbl

[Ge] Getzler (E.). - A short proof of the Atiyah-Singer Index Theorem, Topology, t. 25, 1986, p. 111-117. | MR | Zbl

[GrH] Griffiths (P.), Harris (J.). - Principles of Algebraic Geometry. - Wiley, New-York, 1978. | MR | Zbl

[Grot] Grothendieck (A.). - Sur quelques points d'algèbre homologique, Tôhoku Math. J., t. 9, 1957, p. 119-221. | MR | Zbl

[GS1] Gillet (H.), Soulé (C.). - Analytic torsion and the arithmetic Todd genus, Topology, t. 30, 1991, p. 21-54. | MR | Zbl

[GS2] Gillet (H.), Soulé (C.). - An arithmetic Riemann-Roch Theorem, Invent. Math., t. 110, 1992, p. 473-543. | MR | Zbl

[KM] Knudsen (P.F.), Mumford (D.). - The projectivity of the moduli space of stable curves I, Preliminaires on "det" and "div", Math. Scand., t. 39, 1976, p. 19-55. | Zbl

[Ma] Ma (Xiaonan). - Formes de torsion analytique et familles de submersions, C. R. Acad. Sciences Paris, t. 324, série I, 1997, p. 205-210. | MR | Zbl

[Ma1] Ma (Xiaonan). - Formes de torsion analytique et familles de submersions II, à paraître.

[MKS] Mckean (H.), Singer (I.M.). - Curvature and the eigenvalues of the Laplacian, J. Diff. Geom., t. 1, 1967, p. 43-69. | MR | Zbl

[Q1] Quillen (D.). - Higher K-theories I., Springer Lecture Notes in Math., 341, Springer, Berlin, 1973, p. 85-147. | MR | Zbl

[Q2] Quillen (D.). - Superconnections and the Chern character, Topology, t. 24, 1986, p. 89-95. | MR | Zbl

[RS] Ray (D.B.), Singer (I.M.). - Analytic torsion for complex manifolds, Ann. of Math., t. 98, 1973, p. 154-177. | MR | Zbl

[T] Taylor (M.). - Pseudodifferential operators. - Princeton University Press, Princeton, 1981. | MR | Zbl

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