Equivariant short exact sequences of vector bundles and their analytic torsion forms

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1. [B1] Bismut, J. -M.: Koszul complexes, harmonic oscillators and the Todd class, J. Am. Math. Soc.3 (1990) 159-256. Zbl0702.58071MR1017783
2. [B2] Bismut, J. -M.: Martingales, the Malliavin calculus and hypoellipticity under general Hörmander's conditions, Z. Wahrsh. Verw. Gebiete56 (1981) 469- 505. Zbl0445.60049MR621660
3. [B3] Bismut, J. -M.: The infinitesimal Lefschetz formulas: A heat equation proof, J. Funct. Anal.62 (1985) 435-457. Zbl0572.58021MR794778
4. [B4] Bismut, J. -M.: The index theorem for families of Dirac operators: two heat equation proofs, Invent. Math.83 (1986) 91-151. Zbl0592.58047MR813584
5. [B5] Bismut, J.-M.: Complex equivariant intersection, excess normal bundles and Bott-Chern currents, Comm. Math. Phys.148 (1992) 1—55. Zbl0759.53040
6. [B6] Bismut, J.-M.: On certain infinite dimensional aspects of Arakelov intersection theory, Comm. Math. Phys.148 (1992) 217-248. Zbl0763.53033MR1178144
7. [B7] Bismut, J.-M.: Transformations différentiables du mouvement Brownien, Proc. Conf. in honor of L. Schwartz, Astérisque131 (1985) 61-87. Zbl0572.60074MR816739
8. [B8] Bismut, J.-M.: Torsion analytique équivariante d'une suite exacte courte de fibrés holomorphes, C.R. Acad. Sci. Paris316, série I (1993) 579- 584. Zbl0784.32022MR1212208
9. [B9] Bismut, J.-M.: Métriques de Quillen equivariantes et plongements complexes, C.R. Acad. Sci. Paris316 série I (1993) 827-832. Zbl0773.53026MR1218270
10. [B10] Bismut, J.-M.: Equivariant immersions and Quillen metrics, Preprint Orsay93-56. To appear in J. Jiff. Geom. Zbl0826.32024MR1316553
11. [BGS1] Bismut, J.-M., Gillet, H. and Soulé, C.: Analytic torsion and holomorphic determinant bundles.I, Comm. Math. Phys.115 (1988) 49-78. Zbl0651.32017MR929146
12. [BGS2] Bismut, J.-M., Gillet, H. and Soulé, C.: Analytic torsion and holomorphic determinant bundles. II, Comm. Math. Phys.115 (1988) 79-126. Zbl0651.32017MR929147
13. [BGS3] Bismut, J.-M., Gillet, H. and Soulé, C.: Analytic torsion and holomorphic determinant bundles. III, Comm. Math. Phys.115 (1988) 301-351. Zbl0651.32017MR931666
14. [BL] Bismut, J.-M. and Lebeau, G.: Complex immersions and Quillen metrics, Publ. Math. IHES74 (1991) 1-298. Zbl0784.32010MR1188532
15. [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. Zbl0148.31906MR185607
16. [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. Zbl0529.53018MR765366
17. [F] Faltings, G.: Lectures on the Arithmetic Riemann-Roch Theorem. Princeton Univ. Press, Princeton, 1992. Zbl0744.14016MR1158661
18. [GlJ] Glimm, J. and Jaffe, A.: Quantum Physics, Springer, Berlin, Heidelberg, New York, 1987. Zbl0461.46051MR887102
19. [GS1] Gillet, H. and Soulé, C.: Analytic torsion and the arithmetic Todd genus, Topology31 (1991) 21-54. Zbl0787.14005MR1081932
20. [GS2] Gillet, H. and Soulé, C.: Arithmetic intersection theory, Publ. Math. IHES72 (1990) 93-174. Zbl0741.14012MR1087394
21. [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. Zbl0715.14006MR1038362
22. [GS4] Gillet, H. and Soulé, C.: An arithmetic Riemann-Roch theorem, Invent. Math.110 (1992), 473-543. Zbl0777.14008MR1189489
23. [IkW] Ikeda, N. and Watanabe, S.: Stochastic Differential Equations and Diffusion Processes, North-Holland, Amsterdam, 1981. Zbl0495.60005MR637061
24. [IMK] Itô, K. and McKean, H.: Diffusion processes and their sample paths, Grundl. Math. Wiss., bd. 125, Springer, Berlin, Heidelberg, New York, 1974. Zbl0285.60063MR345224
25. [K] Köhler, K.: Equivariant analytic torsion on P''C, to appear. 
26. [L] Lerch, M.: Note sur la fonction R(w, x, s) = Σ∞0e2πkix /(w+k)s, Acta Math. 11 (1887-1888) 19-24. JFM19.0438.01
27. [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. Zbl0411.60060MR536013
28. [MQ] Mathai, V. and Quillen, D.: Superconnections, Thom classes and equivariant differential forms, Topology25 (1986) 85-110. Zbl0592.55015MR836726
29. [NO] Nikiforov, A. and Ouvarov, V.: Eléments de la théorie des fonctions spéciales, Mir, Moscow, 1976. Zbl0378.33001MR460738
30. [Q1] Quillen, D.: Superconnections and the Chern character, Topology24 (1985) 89-95. Zbl0569.58030MR790678
31. [Q2] Quillen, D.: Determinants of Cauchy-Riemann operators over a Riemann surface, Func. Anal. Appl.14 (1985) 31-34. Zbl0603.32016
32. [RS] Ray, D.B. and Singer, I.M.: Analytic torsion for complex manifolds, Ann. of Math. (2) 98 (1973) 154-177. Zbl0267.32014MR383463
33. [Si1] Simon, B.: Functional Integration and Quantum Physics, Academic Press, New York, 1979. Zbl0434.28013MR544188
34. [Si2] Simon, B.: Notes on infinite determinants of Hilbert space operators, Adv. in Math.24 (1977) 244-273. Zbl0353.47008MR482328
35. [W] Weil, A.: Elliptic functions according to Eisenstein and Kronecker, Erg. Math. Grenzg. 88, Springer, Berlin, Heidelberg, New York, 1976. Zbl0318.33004MR562289

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