Families torsion and Morse functions
Astérisque, no. 275 (2001) , 303 p.
@book{AST_2001__275__R1_0,
     author = {Bismut, Jean-Michel and Goette, Sebastian},
     title = {Families torsion and {Morse} functions},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {275},
     year = {2001},
     mrnumber = {1867006},
     zbl = {1071.58025},
     language = {en},
     url = {http://archive.numdam.org/item/AST_2001__275__R1_0/}
}
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Bismut, Jean-Michel; Goette, Sebastian. Families torsion and Morse functions. Astérisque, no. 275 (2001), 303 p. http://numdam.org/item/AST_2001__275__R1_0/

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

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

[BeV] Berline N., Vergne M. - Zéros d'un champ de vecteurs et classes caractéristiques équivariantes. Duke Math. J., 50, 539-549 (1983). | MR | Zbl

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

[B1] Bismut, J.-M. - Large deviations and the Malliavin calculus. Progress in Mathematics n° 45. Basel-Boston-Stuttgart: Birkhäuser 1984. | MR | Zbl

[B2] Bismut, J.-M. - The Atiyah-Singer theorems: a probabilistic approach. I. J. Funct. Anal., 57, 56-99 (1984). | MR | Zbl | DOI

Bismut, J.-M. - The Atiyah-Singer theorems: a probabilistic approach. II. J. Funct. Anal., 57, 329-348 (1984). | MR | Zbl | DOI

[B3] Bismut, J.-M. - The index Theorem for families of Dirac operators : two heat equation proofs. Invent. Math. 83, 91-151 (1986). | MR | Zbl | EuDML | DOI

[B4] Bismut, J.-M. - Localization formulas, superconnections and the index theorem for families. Comm. Math. Phys., 103, 127-166 (1986). | MR | Zbl | DOI

[B5] Bismut, J.-M. - Formules de Lichnerowicz et théorème de l'indice. Proceedings of the Conference in honour of A. Lichnerowicz, D. Bernard, Y. Choquet-Bruhat eds.. Vol. Géométrie Différentielle, p. 11-31. Travaux en cours. Paris: Hermann 1988. | MR | Zbl

[B6] Bismut, J.-M. - Superconnection currents and complex immersions. Invent. Math., 99, 59-113 (1990). | MR | Zbl | EuDML | DOI

[B7] Bismut, J.-M. - Koszul complexes, harmonic oscillators and the Todd class. J.A.M.S. 3, 159-256 (1990). | MR | Zbl

[B8] Bismut, J.-M. - Equivariant short exact sequences of vector bundles and their analytic torsion forms. Comp. Math., 93, 291-354 (1994). | MR | Zbl | EuDML | Numdam

[B9] Bismut, J.-M. - Equivariant immersions and Quillen metrics. J. Diff. Geom., 41, 53-157 (1995). | MR | Zbl | DOI

[B10] Bismut, J.-M. - Holomorphic families of immersions and higher analytic torsion forms. Astérisque 244. Paris SMF 1997. | MR | Zbl | Numdam

[BF1] Bismut, J.-M., Freed D. - The analysis of elliptic families. I. Metrics and connections on determinant bundles. Comm. Math. Phys., 106, 159-176 (1986). | MR | Zbl | DOI

[BF2] Bismut, J.-M., Freed D. - The analysis of elliptic families. II. Eta invariants and the holonomy theorem. Comm. Math. Phys., 107, 103-163 (1986). | MR | Zbl | DOI

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

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

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

[BGS2] Bismut, J.-M., Gillet, H., Soulé, C. - Bott-Chern currents and complex immersions. Duke Math. Journal, 60, 255-284 (1990). | MR | Zbl | DOI

[BGS3] Bismut, J.-M., Gillet, H., Soulé, C. - Complex immersions and Arakelov geometry. The Grothendieck Festschrift, P. Cartier et al. ed. Vol. I, pp. 249-331. Progress in Math. n° 86. Boston: Birkhaüser 1990. | MR | Zbl

[BGo1] Bismut, J.-M., Goette, S. - Holomorphic equivariant analytic torsions. G.A.F.A., 10, 1289-1422 (2000). | MR | Zbl

[BGo2] Bismut, J.-M., Goette, S. - Rigidité des formes de torsion analytique en théorie de de Rham. CR. Acad. Sci. Paris, Série I, 330, 471-477 (2000). | MR | Zbl

[BGo3] Bismut, J.-M., Goette, S. - Formes de torsion analytique en théorie de de Rham et fonctions de Morse. CR. Acad. Sci. Paris, Série I, 330, 479-484 (2000). | MR | Zbl

[BGo4] Bismut, J.-M., Goette, S. - Torsions analytiques équivariantes en théorie de de Rham. CR. Acad. Sci. Paris, Série I, 332, 33-39 (2001). | MR | Zbl

[BGo5] Bismut, J.-M., Goette, S. - Equivariant de Rham torsions. Preprint Mathématique Orsay 2001-08 (2001). | MR | Zbl

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

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

[Blo1] Bismut, J.-M., Lott, J. - Flat vector bundles, direct images and higher analytic torsion forms. J. Am. Math. Soc., 8, 291-363 (1995). | MR | Zbl | DOI

[BLo2] Bismut, J.-M., Lott, J. - Torus bundles and the group cohomology of G L ( N , ) . J. Diff. Geom., 47, 196-236 (1997). | MR | Zbl | DOI

[BZ1] Bismut, J.-M., Zhang, W. - An extension of a Theorem of Cheeger and Müller. Astérisque, 205, 1992. | MR | Zbl | Numdam

[BZ2] Bismut, J.-M., Zhang, W. - Milnor and Ray-Singer metrics on the equivariant determinant of a flat vector bundle. G.A.F.A., 4, 137-212 (1994). | MR | Zbl | EuDML

[Bo] Bott, R. - A residue formula for holomorphic vector fields. J. Differential Geometry, 1, 311-330 (1967). | MR | Zbl | DOI

[BoCh] Bott, R., Chern, S. S. - Hermitian vector bundles and the equidistribution of the zeroes of their holomorphic sections. Acta Math., 114, 71-112 (1965). | MR | Zbl | DOI

[Bu1] Bunke, U - Higher analytic torsion of sphere bundles and continuous cohomology of Diff (S 2n-1 ). Preprint 1998.

[Bu2] Bunke, U - Equivariant higher analytic torsion and equivariant Euler characteristic. Amer. J. Math., 122, 377-401 (2000). | MR | Zbl | DOI

[CaE] Cartan, H., Eilenberg, S. - Homological Algebra. Princeton: Princeton University Press 1956. | MR | Zbl

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

[ChP] Chazarain, J., Piriou, A. - Introduction à la théorie des équations aux dérivées partielles linéaires. Paris: Gauthiers-Villars 1981. | MR | Zbl

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

[CSi] Cheeger, J., Simons, J. - Differential characters and geometric invariants. Geometry and Topology (J. Alexander and J. Harer eds), Lecture Notes in Mathematics, vol. 1167, 50-80. Berlin-Heidelberg-New-York: Springer 1985. | MR | Zbl | DOI

[Da] Dai, X. - Adiabatic limits, non multiplicativity of signature and Leray spectral sequence. J.A.M.S., 4, 265-321 (1991). | MR | Zbl

[D] Dynkin, E. B. - Diffusion of tensors. Soviet Math. Doklady, 9, 532-535 (1968). | Zbl | MR

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

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

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

[HSj] Helffer, B., Sjöstrand, J. - Puits multiples en mécanique semi-classique IV., Etude du complexe de Witten. Comm. in PDE, 10, 245-340 (1985). | MR | Zbl | DOI

[Hö] Hörmander, L. - The analysis of partial differential operators I. Grundl. Math. Wiss., Band 256. Berlin-Heidelberg-New-York: Springer 1983. | Zbl

[I] Igusa, K. - Parametrized Morse theory and its applications. Proc. Internat. Cong. Math. Kyoto 1990, 643-651. Math. Soc. Japan: Tokyo 1991. | MR | Zbl

[II] Illman, S. - Smooth equivariant triangulations of G-manifolds for G a finite group. Math. Annal., 233, 199-220 (1978). | MR | Zbl | EuDML | DOI

[It] Itô, K. - Stochastic parallel displacement. In Probabilistic methods in differential equations. Lecture Notes in Mathematics n° 451, 1-7. Berlin- Heidelberg-New-York: Springer 1975. | MR | Zbl

[K] Klein, J. - Higher Franz-Reidemeister torsion: low-dimensional applications. Mapping class groups and moduli spaces of Riemann surfaces (Göttingen, 1991/Seattle, WA, 1991), 195-204, Contemp. Math., 150, Providence: Amer. Math. Soc., 1993. | MR | Zbl | DOI

[KöRoe] Köhler, K., Roessler, D. - A fixed point formula of Lefschetz type in Arakelov geometry I. Statement and proofs. Preprint IHES/M/98/76, November 1998. To appear. | MR | Zbl

[La] Laudenbach, F. - On the Thom-Smale complex. Appendix to 'An extension of a theorem by Cheeger and Müller', Astérisque, 205, 219-233 (1992). | MR | Numdam | Zbl

[Le] Lerch, M. - Note sur la fonction ( w , x , s ) = k = 0 e 2 i π k x ( w + k ) s . Acta Math., 11, 19-24 (1887-1888). | MR | JFM | DOI

[LoRo] Lott, J., Rothenberg, M. - Analytic torsion for group actions. J. Diff. Geom., 34, 431-481 (1991). | MR | Zbl | DOI

[Ma1] Ma, X. - Formes de torsion analytique et familles de submersions. Thèse Université Paris-Sud: Orsay 1998. | MR

[Ma2] Ma, X. - Formes de torsion analytique et familles de submersion II. To appear in Asian J. Math.. | MR | Zbl

[Ma3] Ma, X. - Submersions and equivariant Quillen metrics. To appear. | Zbl | MR | Numdam

[Ma4] Ma, X. - Functoriality of real analytic torsion forms. To appear. | MR | Zbl

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

[MazMe] Mazzeo, R., Melrose, R. - The adiabatic limit, Hodge cohomology and Leray's spectral sequence of a fibration. J. Diff. Geom., 31, 185-213 (1990). | MR | Zbl | DOI

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

[Mi1] Milnor, J. - Whitehead torsion. Bull. Am. Math. Soc., 72, 358-426 (1966). | MR | Zbl | DOI

[Mi2] Milnor, J. - Lectures on the h-Cobordism Theorem. Princeton: Princeton University Press 1965. | MR | Zbl | DOI

[Mül] Müller, W. - Analytic torsion and R-torsion of Riemannian manifolds. Adv. in Math., 28, 233-305 (1978). | MR | Zbl | DOI

[Mü2] Müller, W. - Analytic torsion and R-torsion for unimodular representations. J. Amer. Math. Soc., 6, 721-753 (1993). | Zbl | MR | DOI

[PSm] Palis, J., Smale, S. - Structural stability theorems. Global Analysis. Proc. Symp. Pure Math., Vol. XIV, 223-231. Providence: A.M.S. 1970. | MR | Zbl | DOI

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

[Q2] Quillen, D. - Determinants of Cauchy-Riemann operators over a Riemannian surface. Funct. Anal. Appl., 19, 31-34 (1985). | Zbl | DOI

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

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

[ReSi] Reed, M., Simon, B. - Methods of modern Mathematical Physics, Vol. IV: Analysis of operators. Boston: Academic Press 1979. | MR | Zbl

[Rei] Reidemeister, K. - Homotopieringe und Linsenraüm. Hamburger Abhandl., 11, 102-109 (1935). | MR | JFM | DOI

[Ro] Rothenberg, M. - Torsion invariants and finite transformation groups. In Algebraic and Geometric Topology, Part I, 267-311. Proceedings Symp. Pure Math. 32. Providence: AMS 1978. | MR | Zbl | DOI

[Sml] Smale, S. - On gradient dynamical systems. Ann. of Math., 74, 199-206 (1961). | MR | Zbl | DOI

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

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

[Th] Thom, R. - Sur une partition en cellules associée à une fonction sur une variété. CR. Acad. Sci. Paris, 228, 973-975 (1949). | MR | Zbl

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

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

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