This is a preview of subscription content, log in via an institution to check access.
References
[A] Atiyah, M.F.: Circular symmetry and stationary phase approximation. Proceedings of the conference in honor of L. Schwartz. Astérisque131, 43–59 (1985)
[ABP] Atiyah, M.F., Bott, R., Patodi, V.K.: On the heat equation and the index Theorem. Invent Math.19, 279–330 (1973)
[BeV] Berline, N., Vergne, M.: Zéros d'un champ de vecteur et classes caractéristiques équivariantes. Duke Math. J.50, 539–549 (1983)
[B1] Bismut, J.M.: The Atiyah-Singer index theorems: a probabilistic approach. I. J. Funct. Anal.57, 56–99 (1984)
[B2] Bismut, J.M.: Index Theorem and equivariant cohomology on the loop space. Commun. Math. Phys.98, 213–237 (1985)
[B3] Bismut, J.M.: Localization formulas, superconnections, and the Index Theorem for families. Commun. Math. Phys.103, 127–166 (1986)
[B4] Bismut, J.M.: A local index Theorem for non Kähler manifolds. Math. Ann.284, 681–699 (1989)
[BGS1] Bismut, J.M., Gillet, H., Soulé, C.: Analytic torsion and holomorphic determinant bundles I. Bott-Chern forms and analytic torsion. Commun. Math. Phys.115, 49–78 (1988)
[BGS2] Bismut, J.M., Gillet, H., Soulé, C.: Analytic torsion and holomorphic determinant bundles II. Direct images and Bott-Chern forms. Commun. Math. Phys.115, 79–126 (1988)
[BGS3] Bismut, J.M., Gillet, H., Soulé, C.: Analytic torsion and holomorphic determinant bundles III. Quillen metrics and holomorphic determinants. Commun. Math. Phys.115, 301–351 (1988)
[BoC] Bott, R., Chern, S.: Hermitian vector bundles and the equidistribution of the zeros of their holomorphic sections. Acta Math.114, 71–112 (1968)
[D] Donaldson, S.: Anti self-dual Yang-Mills connections over complex algebraic surfaces and stable vector bundles. Proc. Lond. Math. Soc.50, 1–26 (1985)
[DH] Duistermaat, J.J., Heckman, G.: On the variation on the cohomology of the symplectic form of the reduced phase space. Invent. Math.69, 259–268 (1982); Addedum72, 153–158 (1983)
[Gi] Gilkey, P.: Curvature and the eigenvalues of the Laplacian. Adv. Math.10, 344–382 (1973)
[H] Hitchin, N.: Harmonic spinors. Adv. Math.14, 1–55 (1974)
[MKS] Mc, Kean H., Singer, I.M.: Curvature and the eigenvalues of the Laplacian, J. Differ. Geom.1, 43–69 (1967)
[P1] Patodi, V.K.: Curvature and the eigenforms of the Laplacian. J. Differ. Geom.5, 233–249 (1971)
[P2] Patodi, V.K.: Analytic proof of the Riemann-Roch-Hirzebruch Theorem for Kähler manifolds, J. Differ. Geom.5, 251–283 (1971)
[Q] Quillen, D.: Determinants of Cauchy-Riemann operators over a Riemann surface. Funct. Anal. Appl.14, 31–34 (1985)
[RS] Ray, D.B., Singer, I.M.: Analytic torsion for complex manifolds, Ann. Math.98, 154–177 (1973)
Author information
Authors and Affiliations
Additional information
This paper was written while the author was visiting IHES, during the academic year 1987–1988
Rights and permissions
About this article
Cite this article
Bismut, JM. Equivariant Bott-Chern currents and the Ray-Singer analytic torsion. Math. Ann. 287, 495–507 (1990). https://doi.org/10.1007/BF01446907
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01446907