@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/} }
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] On the heat equation and the index theorem. Invent Math. 19, 279-330 (1973). | MR | Zbl | EuDML | DOI
, , -[BeGeV] Heat kernels and Dirac operators. Grundl. Math. Wiss. Band 298. Berlin-Heidelberg-New-York: Springer 1992. | MR | Zbl
, , -[BeV] Zéros d'un champ de vecteurs et classes caractéristiques équivariantes. Duke Math. J., 50, 539-549 (1983). | MR | Zbl
, -[BerB] Quillen metrics and higher analytic torsion forms. J. Reine Angew. Math., 457, 85-184 (1994). | MR | Zbl | EuDML
, -[B1] Large deviations and the Malliavin calculus. Progress in Mathematics n° 45. Basel-Boston-Stuttgart: Birkhäuser 1984. | MR | Zbl
-[B2] The Atiyah-Singer theorems: a probabilistic approach. I. J. Funct. Anal., 57, 56-99 (1984). | MR | Zbl | DOI
-The Atiyah-Singer theorems: a probabilistic approach. II. J. Funct. Anal., 57, 329-348 (1984). | MR | Zbl | DOI
-[B3] The index Theorem for families of Dirac operators : two heat equation proofs. Invent. Math. 83, 91-151 (1986). | MR | Zbl | EuDML | DOI
-[B4] Localization formulas, superconnections and the index theorem for families. Comm. Math. Phys., 103, 127-166 (1986). | MR | Zbl | DOI
-[B5] 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] Superconnection currents and complex immersions. Invent. Math., 99, 59-113 (1990). | MR | Zbl | EuDML | DOI
-[B7] Koszul complexes, harmonic oscillators and the Todd class. J.A.M.S. 3, 159-256 (1990). | MR | Zbl
-[B8] Equivariant short exact sequences of vector bundles and their analytic torsion forms. Comp. Math., 93, 291-354 (1994). | MR | Zbl | EuDML | Numdam
-[B9] Equivariant immersions and Quillen metrics. J. Diff. Geom., 41, 53-157 (1995). | MR | Zbl | DOI
-[B10] Holomorphic families of immersions and higher analytic torsion forms. Astérisque 244. Paris SMF 1997. | MR | Zbl | Numdam
-[BF1] The analysis of elliptic families. I. Metrics and connections on determinant bundles. Comm. Math. Phys., 106, 159-176 (1986). | MR | Zbl | DOI
, -[BF2] The analysis of elliptic families. II. Eta invariants and the holonomy theorem. Comm. Math. Phys., 107, 103-163 (1986). | MR | Zbl | DOI
, -[BGS1] Analytic torsion and holomorphic determinant bundles, I. Comm. Math. Phys., 115, 49-78 (1988). | MR | Zbl | DOI
, , -Analytic torsion and holomorphic determinant bundles, II. Comm. Math. Phys., 115, 79-126 (1988). | Zbl | DOI
, , -Analytic torsion and holomorphic determinant bundles, III. Comm. Math. Phys., 115, 301-351 (1988). | MR | Zbl | DOI
, , -[BGS2] Bott-Chern currents and complex immersions. Duke Math. Journal, 60, 255-284 (1990). | MR | Zbl | DOI
, , -[BGS3] 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] Holomorphic equivariant analytic torsions. G.A.F.A., 10, 1289-1422 (2000). | MR | Zbl
, -[BGo2] Rigidité des formes de torsion analytique en théorie de de Rham. CR. Acad. Sci. Paris, Série I, 330, 471-477 (2000). | MR | Zbl
, -[BGo3] 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] Torsions analytiques équivariantes en théorie de de Rham. CR. Acad. Sci. Paris, Série I, 332, 33-39 (2001). | MR | Zbl
, -[BGo5] Equivariant de Rham torsions. Preprint Mathématique Orsay 2001-08 (2001). | MR | Zbl
, -[BK] Higher analytic torsion forms for direct images and anomaly formulas. J. Alg. Geom., 1, 647-684 (1992). | MR | Zbl
, -[BL] Complex immersions and Quillen metrics. Publ Math. IHES, 74, 1-297 (1991). | MR | Zbl | EuDML | Numdam | DOI
, -[Blo1] Flat vector bundles, direct images and higher analytic torsion forms. J. Am. Math. Soc., 8, 291-363 (1995). | MR | Zbl | DOI
, -[BLo2] Torus bundles and the group cohomology of . J. Diff. Geom., 47, 196-236 (1997). | MR | Zbl | DOI
, -[BZ1] An extension of a Theorem of Cheeger and Müller. Astérisque, 205, 1992. | MR | Zbl | Numdam
, -[BZ2] 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] A residue formula for holomorphic vector fields. J. Differential Geometry, 1, 311-330 (1967). | MR | Zbl | DOI
-[BoCh] Hermitian vector bundles and the equidistribution of the zeroes of their holomorphic sections. Acta Math., 114, 71-112 (1965). | MR | Zbl | DOI
, -[Bu1] Higher analytic torsion of sphere bundles and continuous cohomology of Diff . Preprint 1998.
-[Bu2] Equivariant higher analytic torsion and equivariant Euler characteristic. Amer. J. Math., 122, 377-401 (2000). | MR | Zbl | DOI
-[CaE] Homological Algebra. Princeton: Princeton University Press 1956. | MR | Zbl
, -[Ce] 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] Introduction à la théorie des équations aux dérivées partielles linéaires. Paris: Gauthiers-Villars 1981. | MR | Zbl
, -[C] Analytic torsion and the heat equation. Ann. of Math., 109, 259-322 (1979). | MR | Zbl | DOI
-[CSi] 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] Adiabatic limits, non multiplicativity of signature and Leray spectral sequence. J.A.M.S., 4, 265-321 (1991). | MR | Zbl
-[D] Diffusion of tensors. Soviet Math. Doklady, 9, 532-535 (1968). | Zbl | MR
-[Ge] A short proof of the Atiyah-Singer Index Theorem. Topology, 25, 111-117 (1986). | MR | Zbl | DOI
-[GS1] Analytic torsion and the arithmetic Todd genus. Topology, 30, 21-54 (1991). | MR | Zbl | DOI
, -[GS2] An arithmetic Riemann-Roch theorem. Invent. Math., 110, 473-543 (1992). | MR | Zbl | EuDML | DOI
-[HSj] Puits multiples en mécanique semi-classique IV., Etude du complexe de Witten. Comm. in PDE, 10, 245-340 (1985). | MR | Zbl | DOI
, -[Hö] The analysis of partial differential operators I. Grundl. Math. Wiss., Band 256. Berlin-Heidelberg-New-York: Springer 1983. | Zbl
-[I] Parametrized Morse theory and its applications. Proc. Internat. Cong. Math. Kyoto 1990, 643-651. Math. Soc. Japan: Tokyo 1991. | MR | Zbl
-[II] Smooth equivariant triangulations of -manifolds for a finite group. Math. Annal., 233, 199-220 (1978). | MR | Zbl | EuDML | DOI
-[It] 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] 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] 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] 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] Note sur la fonction . Acta Math., 11, 19-24 (1887-1888). | MR | JFM | DOI
-[LoRo] Analytic torsion for group actions. J. Diff. Geom., 34, 431-481 (1991). | MR | Zbl | DOI
, -[Ma1] Formes de torsion analytique et familles de submersions. Thèse Université Paris-Sud: Orsay 1998. | MR
-[Ma2] Formes de torsion analytique et familles de submersion II. To appear in Asian J. Math.. | MR | Zbl
-[Ma3] Submersions and equivariant Quillen metrics. To appear. | Zbl | MR | Numdam
-[Ma4] Functoriality of real analytic torsion forms. To appear. | MR | Zbl
-[MQ] Superconnections, Thom classes, and equivariant Differential forms. Topology, 25, 85-110 (1986). | MR | Zbl | DOI
-[MazMe] The adiabatic limit, Hodge cohomology and Leray's spectral sequence of a fibration. J. Diff. Geom., 31, 185-213 (1990). | MR | Zbl | DOI
, -[MKeS] Curvature and the eigenvalues of the Laplacian. J. Diff. Geom., 1, 43-69 (1967). | MR | Zbl | DOI
, -[Mi1] Whitehead torsion. Bull. Am. Math. Soc., 72, 358-426 (1966). | MR | Zbl | DOI
-[Mi2] Lectures on the -Cobordism Theorem. Princeton: Princeton University Press 1965. | MR | Zbl | DOI
-[Mül] Analytic torsion and -torsion of Riemannian manifolds. Adv. in Math., 28, 233-305 (1978). | MR | Zbl | DOI
-[Mü2] Analytic torsion and -torsion for unimodular representations. J. Amer. Math. Soc., 6, 721-753 (1993). | Zbl | MR | DOI
-[PSm] Structural stability theorems. Global Analysis. Proc. Symp. Pure Math., Vol. XIV, 223-231. Providence: A.M.S. 1970. | MR | Zbl | DOI
, -[Q1] Superconnections and the Chern character. Topology , 24, 89-95 (1985). | MR | Zbl | DOI
-[Q2] Determinants of Cauchy-Riemann operators over a Riemannian surface. Funct. Anal. Appl., 19, 31-34 (1985). | Zbl | DOI
-[RS1] -torsion and the Laplacian for Riemannian manifolds. Adv. in Math., 7, 145-210 (1971). | MR | Zbl | DOI
, -[RS2] Analytic torsion for complex manifolds. Ann. of Math., 98, 154-177 (1973). | MR | Zbl | DOI
, -[ReSi] Methods of modern Mathematical Physics, Vol. IV: Analysis of operators. Boston: Academic Press 1979. | MR | Zbl
, -[Rei] Homotopieringe und Linsenraüm. Hamburger Abhandl., 11, 102-109 (1935). | MR | JFM | DOI
-[Ro] 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] On gradient dynamical systems. Ann. of Math., 74, 199-206 (1961). | MR | Zbl | DOI
-[Sm2] Differentiable dynamical systems. Bull. Am. Math. Soc., 73, 747-817 (1967). | MR | Zbl | DOI
-[T] Pseudodifferential operators. Princeton: Princeton University Press 1981. | MR | Zbl
-[Th] Sur une partition en cellules associée à une fonction sur une variété. CR. Acad. Sci. Paris, 228, 973-975 (1949). | MR | Zbl
-[V] Diffusion processes in a small time interval. Comm. Pure Appl. Math., 20, 659-685 (1967). | MR | Zbl | DOI
-[We] Elliptic functions according to Eisenstein and Kronecker. Erg. Math. Grenzg. 88. Berlin-Heidelberg-New-York: Springer 1976. | MR | Zbl
-[W] Supersymmetry and Morse theory. J. Diff. Geom., 17, 661-692 (1982). | MR | Zbl | DOI
-