An extension of a theorem by Cheeger and Müller

Bismut, Jean-Michel ; Zhang, Weiping

An extension of a Theorem by Cheeger and Müller, Astérisque, no. 205 (1992), pp. 7-218.

complété par Appendix. On the Thom-Smale complex

MR Zbl | 14 citations dans Numdam

@incollection{AST_1992__205__7_0,
     author = {Bismut, Jean-Michel and Zhang, Weiping},
     title = {An extension of a theorem by {Cheeger} and {M\"uller}},
     booktitle = {An extension of a Theorem by Cheeger and M\"uller},
     series = {Ast\'erisque},
     pages = {7--218},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {205},
     year = {1992},
     mrnumber = {1185803},
     zbl = {0781.58039},
     language = {en},
     url = {http://www.numdam.org/item/AST_1992__205__7_0/}
}

TY  - CHAP
AU  - Bismut, Jean-Michel
AU  - Zhang, Weiping
TI  - An extension of a theorem by Cheeger and Müller
BT  - An extension of a Theorem by Cheeger and Müller
AU  - Collectif
T3  - Astérisque
PY  - 1992
SP  - 7
EP  - 218
IS  - 205
PB  - Société mathématique de France
UR  - http://www.numdam.org/item/AST_1992__205__7_0/
LA  - en
ID  - AST_1992__205__7_0
ER  -

%0 Book Section
%A Bismut, Jean-Michel
%A Zhang, Weiping
%T An extension of a theorem by Cheeger and Müller
%B An extension of a Theorem by Cheeger and Müller
%A Collectif
%S Astérisque
%D 1992
%P 7-218
%N 205
%I Société mathématique de France
%U http://www.numdam.org/item/AST_1992__205__7_0/
%G en
%F AST_1992__205__7_0

Bismut, Jean-Michel; Zhang, Weiping. An extension of a theorem by Cheeger and Müller, dans An extension of a Theorem by Cheeger and Müller, Astérisque, no. 205 (1992), pp. 7-218. http://www.numdam.org/item/AST_1992__205__7_0/

Bibliographie
Cité par

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

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

[B1] Bismut J.-M., Superconnection currents and complex immersions, Invent. Math. 99 (1990), 59-113. | DOI | EuDML | MR | Zbl

[B2] Bismut J.-M., Large deviations and the Malliavin calculus, Progress in Math. Vol. 45, Boston : Birkhaüser 1984. | MR | Zbl

[B3] Bismut J.-M., From Quillen metrics to Reidemeister metrics: some aspects of the Ray-Singer analytic torsion, To appear. | MR | Zbl

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

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

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

[BGS4] Bismut J.-M., Gillet H., Soulé C., Complex immersions and Arakelov geometry, The Grothendieck Festschrift, P. Cartier and al. ed., vol. I, pp. 249-331, Progress in Math. n. 86, Boston : Birkhaüser 1990. | MR | Zbl

[BL1] Bismut J.-M., Lebeau G., Immersions complexes et métriques de Quillen, C.R. Acad. Sci. Paris Sér. I. Math. 309 (1989), 487-491. | MR | Zbl

[BL2] Bismut J.-M., Lebeau G., Complex immersions and Quillen metrics, Prépublications d'Orsay 90-13 (1990), To appear in Publ. Math. IHES.

[BZ] Bismut J.-M., Zhang W., Métriques de Reidemeister et métriques de Ray- Singer sur le déterminant de la cohomologie d'un fibré plat : une extension d'un résultat de Cheeger et Müller. C.R. Acad. Sci. Paris, t. 313, Série I, (1991), 775-782.

[C] Cheeger J., Analytic torsion and the heat equation. Ann. of Math. 109 (1979), 259-322.

[Ce] Cerf J., La stratification naturelle des espaces de fonctions différentiables réelles et le théorème de la pseudo-isotopie, Publ. Math. IHES, 39 (1970), 5-173.

[D] Dai X., Geometric invariants and their adiabatic limits, Preprint 1991.

[F] Franz W., Uber die Torsion einer überdeckrung, J. Reine Angew. Math. 173 (1935), 245-254.

[G] Getzler E., A short proof of the Atiyah-Singer index theorem, Topology 25 (1986), 111-117.

[GlJ] Glimm J., Jaffe A., Quantum physics. Berlin-Heidelberg-New-York : Springer 1987.

[HSj1] Helffer B., Sjöstrand J., Multiple wells in the semi-classical limit I, Comm. P.D.E. 9 (1984), 337-408.

[HSj2] Helffer B., Sjöstrand J., Puits multiples en limite semi-classique II, Annales I.H.P. (Physique théorique), 42 (1985), 127-212.

[HSj3] Helffer B., Sjöstrand J., Multiple wells in the semi-classical limit III, Math. Nachr. 124 (1985), 263-313.

[HSj4] Helffer B., Sjöstrand J., Puits multiples en mécanique semi-classique, IV. Etude du complexe de Witten, Comm. P.D.E., 10 (1985), 245-340.

[Ho] Hörmander L., The analysis of linear partial differential operators I, Gründl. Math. Wiss. Band 256, Berlin-Heidelberg-New-York : Springer 1983.

[KMu] Knudsen F. F., Mumford D., The projectivity of the moduli space of stable curves, I: Preliminaries on "det" and "div", Math. Scand. 39 (1976), 19-55.

[L] Lichnerowicz A., Spineurs harmoniques, C.R. Acad. Sci. Paris, t. 257, Série A, (1963), 7-9.

[McKS] Mckean H., Singer I. M., Curvature and the eigenforms of the Laplacian, J. Diff. Geom. 1 (1967), 43-69.

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

[Mil] Milnor J., Whitehead torsion, Bull. Amer. Math. Soc. 72 (1966), 358-426.

[Mi2] Milnor J., A duality theorem for Reidemeister torsion, Ann. of Math. 76 (1962), 137-147.

[Mü1] Müller W., Analytic torsion and R-torsion of Riemannian manifolds, Adv. in Math. 28 (1978), 233-305.

[Mü2] Müller W., Analytic torsion and R-torsion for unimodular representations, Preprint MPI 91-50 (1991).

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

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

[R] Ray D. B., Reidemeister torsion and the Laplacian on lens spaces, Adv. in Math. 4 (1970), 109-126.

[RS1] Ray D. B., Singer I. M., $R$ -torsion and the Laplacian on Riemannian manifolds, Adv. in Math. 7 (1971), 145-210.

[RS2] Ray D. B., Singer I. M., Analytic torsion for complex manifolds. Ann. of Math. 98 (1973), 154-177.

[Re] Reidemeister K., Homotopieringe und Linsenraüm, Hamburger Abhandl. 11 (1935), 102-109.

[Rh1] De Rham G., Complexes a automorphismes et homotopies différentiables, Ann. Inst. Fourier 2 (1950), 51-67.

[Rh2] De Rham G., Differentiable manifolds, Berlin-Heidelberg-New-York : Springer 1984.

[Ro] Rosenberg H., A generalization of Morse-Smale inequalities, Bull. Am. Math. Soc. 70 (1964), 422-427.

[Se] Seeley R. T., Complex powers of an elliptic operator, Proc. Symp. Pure and Appl. Math. AMS 10 (1967), 288-307.

[Sm1] Smale S., On gradient dynamical systems, Ann. of Math. 74 (1961), 199-206.

[Sm2] Smale S., Differentiable dynamical systems, Bull. Am. Math. Soc. 73 (1967), 747-817.

[Ta] Tangerman F., Reidemeister torsion and analytic torsion, Preprint 1988.

[Tay] Taylor M., Pseudodifferential operators, Princeton : Princeton University Press 1981.

[T] Thom R., Sur une partition en cellules associée à une fonction sur une variété, C.R. Acad. Sci. Paris. t. 228, Série A, (1949), 661-692.

[V] Varadhan S. R. S., Diffusion processes in a small time interval, Comm. Pure Appl. Math. 20 (1967), 659-685.

[W] Witten E., Supersymmetry and Morse theory, J. of Diff. Geom. 17 (1982), 661-692.