Flat vector bundles and analytic torsion forms
Séminaire de théorie spectrale et géométrie, Volume 19 (2000-2001), pp. 25-40. 
@article{TSG_2000-2001__19__25_0,
     author = {Xiaonan Ma},
     title = {Flat vector bundles and analytic torsion forms},
     journal = {S\'eminaire de th\'eorie spectrale et g\'eom\'etrie},
     pages = {25--40},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {19},
     year = {2000-2001},
     doi = {10.5802/tsg.316},
     zbl = {1004.58020},
     mrnumber = {1909074},
     language = {en},
     url = {https://proceedings.centre-mersenne.org/articles/10.5802/tsg.316/}
}
TY  - JOUR
AU  - Xiaonan Ma
TI  - Flat vector bundles and analytic torsion forms
JO  - Séminaire de théorie spectrale et géométrie
PY  - 2000-2001
SP  - 25
EP  - 40
VL  - 19
PB  - Institut Fourier
PP  - Grenoble
UR  - https://proceedings.centre-mersenne.org/articles/10.5802/tsg.316/
DO  - 10.5802/tsg.316
LA  - en
ID  - TSG_2000-2001__19__25_0
ER  - 
%0 Journal Article
%A Xiaonan Ma
%T Flat vector bundles and analytic torsion forms
%J Séminaire de théorie spectrale et géométrie
%D 2000-2001
%P 25-40
%V 19
%I Institut Fourier
%C Grenoble
%U https://proceedings.centre-mersenne.org/articles/10.5802/tsg.316/
%R 10.5802/tsg.316
%G en
%F TSG_2000-2001__19__25_0
Xiaonan Ma. Flat vector bundles and analytic torsion forms. Séminaire de théorie spectrale et géométrie, Volume 19 (2000-2001), pp. 25-40. doi : 10.5802/tsg.316. https://proceedings.centre-mersenne.org/articles/10.5802/tsg.316/

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

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

[3] Bismut J.-M., Families of immersions, and higher analytic torsion, Astérisque 244, 1997. | MR | Zbl

[4] Bismut J.-M. and Goette S., Families torsion and Morse fonctions, Astérisque 275, 2001. | MR | Zbl

[5] Bismut J.-M. and Lebeau G., Complex immersions and Quillen metrics, Publ. Math. IHES., Vol. 74, 1991, 1-297. | Numdam | MR | Zbl

[6] Bismut J.-M. and Lott J., Flat vector bundles, direct images and higher real analytic torsion, J.A.M.S. 8 ( 1995), 291-363. | MR | Zbl

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

[8] Bunke U., On the functoriality of Lott's secondary analytic index, math. DG/0003171. | Zbl

[9] Cheeger J., Analytic torsion and the Heat Equation, Ann of Math, 109 ( 1979), 259-322. | MR | Zbl

[10] Dai X., Geometric Invariants and Their Adiabatic Limits, Proc. Symposia Pure Math. 54 ( 1993), part II, 145-156. | MR | Zbl

[11] Dai X., Melrose R.B., Adiabatic limit of the analytic torsion, Preprint.

[12] Dwyer W., Weiss M., Williams B., A Parametrized Index Theorem for the Algebraic K-Theory Euler Class, http://www.math.uiuc.edu/K-theory/0086/index.html. | Zbl

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

[14] Griffiths P., Harris J., Principles of Algebraic Geometry, New-York, Wiley 1978. | MR | Zbl

[15] Grothendieck A., Sur quelques points d'algèbre homologique, Tôhoku Math. J. 9, 1957, 119-221. | MR | Zbl

[16] Igusa K., Parametrized Morse theory and its applications. Proceedings of the International Congress of Mathematicians, Vol. I, II (Kyoto, 1990), 643-651, Math. Soc. Japan, Tokyo, 1991. | MR | Zbl

[17] 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, Amer. Math. Soc., Providence, RI, 1993. | MR | Zbl

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

[19] Köhler K., Equivariant Reidemeister torsion on symmetric spaces, Math. Ann. 307 ( 1997), 57-69. | MR | Zbl

[20] Lott J., Secondary analytic indices, Regulars in analysis, Geometry and Number Theory. N.Schappacher, A Reznikov(ed), Progress in Math. 171. Birkhäuse 2000. | MR | Zbl

[21] Lück W., Schick T., and Thielmann T., Torsion and fibrations, J. Reine Angew. Math, 498 ( 1998), 1-33. | MR | Zbl

[22] Ma X., Formes de torsion analytique et familles de submersions I, Bull. Soc. Math. France, 127 ( 1999), 541 -621. | Numdam | MR | Zbl

[23] Ma X., Formes de torsion analytique et familles de submersions II, Asian J of Math, 4 ( 2000), 633-668. | MR | Zbl

[24] Ma X., Functoriality of real analytic torsion forms. Israel J of Math, to appear. | MR | Zbl

[25] Milnor J., Whitehead torsion. Bull. Amer. Math. Soc. 72 1966 358-426. | MR | Zbl

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

[27] Muller W., Analytic torsion and R-torsion for unimodular representations, J.A.M.S, 6 ( 1993), 721-753. | MR | Zbl

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

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

[30] De Rham G., Complexes à automorphismes et homéomorphie différentiable. Ann. Inst. Fourier Grenoble 2 ( 1950), 51-67 ( 1951). | Numdam | MR | Zbl

Cited by Sources: