Equivariant short exact sequences of vector bundles and their analytic torsion forms
Compositio Mathematica, Volume 93 (1994) no. 3, pp. 291-354.
@article{CM_1994__93_3_291_0,
author = {Bismut, Jean-Michel},
title = {Equivariant short exact sequences of vector bundles and their analytic torsion forms},
journal = {Compositio Mathematica},
pages = {291--354},
volume = {93},
number = {3},
year = {1994},
zbl = {0817.32014},
mrnumber = {1300765},
language = {en},
url = {http://archive.numdam.org/item/CM_1994__93_3_291_0/}
}
TY  - JOUR
AU  - Bismut, Jean-Michel
TI  - Equivariant short exact sequences of vector bundles and their analytic torsion forms
JO  - Compositio Mathematica
PY  - 1994
DA  - 1994///
SP  - 291
EP  - 354
VL  - 93
IS  - 3
UR  - http://archive.numdam.org/item/CM_1994__93_3_291_0/
UR  - https://zbmath.org/?q=an%3A0817.32014
UR  - https://www.ams.org/mathscinet-getitem?mr=1300765
LA  - en
ID  - CM_1994__93_3_291_0
ER  - 
%0 Journal Article
%A Bismut, Jean-Michel
%T Equivariant short exact sequences of vector bundles and their analytic torsion forms
%J Compositio Mathematica
%D 1994
%P 291-354
%V 93
%N 3
%G en
%F CM_1994__93_3_291_0
Bismut, Jean-Michel. Equivariant short exact sequences of vector bundles and their analytic torsion forms. Compositio Mathematica, Volume 93 (1994) no. 3, pp. 291-354. http://archive.numdam.org/item/CM_1994__93_3_291_0/

[B1] Bismut, J. -M.: Koszul complexes, harmonic oscillators and the Todd class, J. Am. Math. Soc. 3 (1990) 159-256. | MR | Zbl

[B2] Bismut, J. -M.: Martingales, the Malliavin calculus and hypoellipticity under general Hörmander's conditions, Z. Wahrsh. Verw. Gebiete 56 (1981) 469- 505. | MR | Zbl

[B3] Bismut, J. -M.: The infinitesimal Lefschetz formulas: A heat equation proof, J. Funct. Anal. 62 (1985) 435-457. | MR | Zbl

[B4] Bismut, J. -M.: The index theorem for families of Dirac operators: two heat equation proofs, Invent. Math. 83 (1986) 91-151. | MR | Zbl

[B5] Bismut, J.-M.: Complex equivariant intersection, excess normal bundles and Bott-Chern currents, Comm. Math. Phys. 148 (1992) 1-55. | Zbl

[B6] Bismut, J.-M.: On certain infinite dimensional aspects of Arakelov intersection theory, Comm. Math. Phys. 148 (1992) 217-248. | MR | Zbl

[B7] Bismut, J.-M.: Transformations différentiables du mouvement Brownien, Proc. Conf. in honor of L. Schwartz, Astérisque 131 (1985) 61-87. | MR | Zbl

[B8] Bismut, J.-M.: Torsion analytique équivariante d'une suite exacte courte de fibrés holomorphes, C.R. Acad. Sci. Paris 316, série I (1993) 579- 584. | MR | Zbl

[B9] Bismut, J.-M.: Métriques de Quillen equivariantes et plongements complexes, C.R. Acad. Sci. Paris 316 série I (1993) 827-832. | MR | Zbl

[B10] Bismut, J.-M.: Equivariant immersions and Quillen metrics, Preprint Orsay 93-56. To appear in J. Jiff. Geom. | MR | Zbl

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

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

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

[BL] Bismut, J.-M. and Lebeau, G.: Complex immersions and Quillen metrics, Publ. Math. IHES 74 (1991) 1-298. | Numdam | MR | Zbl

[BoC] Bott, R. and Chern, S.S.: Hermitian vector bundles and the equidistribution of the zeros of their holomorphic sections, Acta Math. 114 (1968) 71-112. | MR | Zbl

[D] Donaldson, S.: Anti-self-dual Yang-Mills connections over complex algebraic surfaces and stable vector bundles, Proc. London Math. Soc. 50 (1985) 1-26. | MR | Zbl

[F] Faltings, G.: Lectures on the Arithmetic Riemann-Roch Theorem. Princeton Univ. Press, Princeton, 1992. | MR | Zbl

[GlJ] Glimm, J. and Jaffe, A.: Quantum Physics, Springer, Berlin, Heidelberg, New York, 1987. | MR | Zbl

[GS1] Gillet, H. and Soulé, C.: Analytic torsion and the arithmetic Todd genus, Topology 31 (1991) 21-54. | MR | Zbl

[GS2] Gillet, H. and Soulé, C.: Arithmetic intersection theory, Publ. Math. IHES 72 (1990) 93-174. | Numdam | MR | Zbl

[GS3] Gillet, H. and Soulé, C.: Characteristic classes for algebraic vector bundles with Hermitian metrics. I, Ann. Math. 131 (1990) 163-203; II, 131 (1990) 205-238. | MR | Zbl

[GS4] Gillet, H. and Soulé, C.: An arithmetic Riemann-Roch theorem, Invent. Math. 110 (1992), 473-543. | MR | Zbl

[IkW] Ikeda, N. and Watanabe, S.: Stochastic Differential Equations and Diffusion Processes, North-Holland, Amsterdam, 1981. | MR | Zbl

[IMK] Itô, K. and Mckean, H.: Diffusion processes and their sample paths, Grundl. Math. Wiss., bd. 125, Springer, Berlin, Heidelberg, New York, 1974. | MR | Zbl

[K] Köhler, K.: Equivariant analytic torsion on P''C, to appear.

[L] Lerch, M.: Note sur la fonction R(w, x, s) = Σ∞0e2πkix /(w+k)s, Acta Math. 11 (1887-1888) 19-24. | JFM

[Ma] Malliavin, P.: Stochastic calculus of variations and hypoelliptic operators, Proc. Conf. on Stochastic Differential Equations, Kyoto (1976); Wiley, New York (1978) pp. 195-263. | MR | Zbl

[MQ] Mathai, V. and Quillen, D.: Superconnections, Thom classes and equivariant differential forms, Topology 25 (1986) 85-110. | MR | Zbl

[NO] Nikiforov, A. and Ouvarov, V.: Eléments de la théorie des fonctions spéciales, Mir, Moscow, 1976. | MR | Zbl

[Q1] Quillen, D.: Superconnections and the Chern character, Topology 24 (1985) 89-95. | MR | Zbl

[Q2] Quillen, D.: Determinants of Cauchy-Riemann operators over a Riemann surface, Func. Anal. Appl. 14 (1985) 31-34. | Zbl

[RS] Ray, D.B. and Singer, I.M.: Analytic torsion for complex manifolds, Ann. of Math. (2) 98 (1973) 154-177. | MR | Zbl

[Si1] Simon, B.: Functional Integration and Quantum Physics, Academic Press, New York, 1979. | MR | Zbl

[Si2] Simon, B.: Notes on infinite determinants of Hilbert space operators, Adv. in Math. 24 (1977) 244-273. | MR | Zbl

[W] Weil, A.: Elliptic functions according to Eisenstein and Kronecker, Erg. Math. Grenzg. 88, Springer, Berlin, Heidelberg, New York, 1976. | MR | Zbl