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Orbifolds and analytic torsions

Author(s): Xiaonan Ma
Journal: Trans. Amer. Math. Soc. 357 (2005), 2205-2233.
MSC (2000): Primary 57J52, 32L10, 58J20
Posted: January 31, 2005
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Abstract | References | Similar articles | Additional information

Abstract: In this paper, we calculate the behavior of the Quillen metric by orbifold immersions. We thus extend a formula of Bismut-Lebeau to the orbifold case.

ESUMÉ. Dans cet article, on calcule le comportement de métrique de Quillen par immersions d'orbifold. On étend ainsi une formule de Bismut-Lebeau au cas d'orbifold.


References:

1.
Adem A., Morava J. and Ruan Y. (Eds), Orbifolds in mathematics and physics. Contemporary Mathematics 310 (2002). MR 1950939 (2003g:00020)

2.
Berline N., Getzler E., and Vergne M., Heat kernels and Dirac operators, Grundl. Math. Wiss. 298, Springer, Berlin-Heidelberg-New York 1992. MR 1215720 (94e:58130)

3.
Bismut J.-M., Superconnection currents and complex immersions, Invent. Math. 99 (1990), 59-113. MR 1029391 (91b:58240)

4.
Bismut J.-M., Koszul complexes, harmonic oscillators and the Todd class, J.A.M.S. 3 (1990), 159-256. MR 1017783 (91b:58245)

5.
Bismut J.-M., Equivariant short exact sequences of vector bundles and their analytic torsion forms. Comp. Math. 93 (1994), 291-354. MR 1300765 (96g:58201)

6.
Bismut J.-M., Equivariant immersions and Quillen metrics, J. Diff. Geom. 41 (1995), 53-159. MR 1316553 (96m:58261)

7.
Bismut J.-M., Families of immersions, and higher analytic torsion, Astérisque 244, 1997. MR 1623496 (2000b:58057)

8.
Bismut J.-M., Gillet H., Soulé C., Analytic torsion and holomorphic determinant bundles. I, Comm. Math. Phys. 115 (1988), 49-78.MR 0929146 (89g:58192a)

9.
Bismut J.-M., Gillet H., Soulé C., Analytic torsion and holomorphic determinant bundles. II, Comm. Math. Phys. 115 (1988), 79-126. MR 0929146 (89g:58192a)

10.
Bismut J.-M., Gillet H., Soulé C., Analytic torsion and holomorphic determinant bundles. III, Comm. Math. Phys. 115 (1988), 301-351.MR 0931666 (89g:58192c)

11.
Bismut J.-M., Gillet H., Soulé C., Bott-Chern currents and complex immersions, Duke Math. Journal 60 (1990), 255-284. MR 1047123 (91d:58239)

12.
Bismut J.-M., Köhler K., Higher analytic torsion forms for direct images and anomaly formulas. J. of. Alg. Geom. 1 (1992), 647-684.MR 1174905 (94a:58209)

13.
Bismut J.-M. and Lebeau G., Complex immersions and Quillen metrics. Publ. Math. IHES., Vol. 74, 1991, 1-297. MR 1188532 (94a:58205)

14.
Bismut J.-M. and Ma X., Holomorphic immersions and equivariant torsion forms, J. Reine Angew. Math. 575 (2004), 189-235. MR 2097553

15.
Cartan H., Quotient d'un espace analytique par un groupe d'automorphismes. Algebraic Geometry and Topology. Fox R.H., Spencer D.C., and Tucker A.W. eds. Princeton Univ Press, Princeton 1957, 90-102.MR 0084174 (18:823b)

16.
Cartan H., and Eilenberg S., Homological Algebra, Princeton 1956.MR 0077480 (17:1040e)

17.
Grothendieck A., Sur quelques points d'algèbre homologique, Tôhoku Math. J. 9 (1957), 119-221. MR 0102537 (21:1328)

18.
Gillet H., Soulé C., Analytic torsion and the arithmetic Todd genus, Topology 30 (1991), 21-54. MR 1081932 (92d:14015)

19.
Gillet H., Soulé C., An arithmetic Riemann-Roch Theorem, Invent. Math. 110 (1992), 473-543. MR 1189489 (94f:14019)

20.
Kawasaki T., The Signature theorem for V-manifolds. Topology 17 (1978), 75-83.MR 0474432 (57:14072)

21.
Kawasaki T., The Riemann-Roch theorem for V-manifolds. Osaka J. Math. 16 (1979), 151-159.MR 0527023 (80f:58042)

22.
Kawasaki T., The Index of elliptic operators for V-manifolds. Nagoya. Math. J. 84 (1981), 135-157.MR 0641150 (83i:58095)

23.
Knudsen P.F., Mumford D., The projectivity of the moduli space of stable curves, I, Preliminaires on ``det'' and ``div'', Math. Scand. 39 (1976), 19-55.MR 0437541 (55:10465)

24.
Köhler K., Roessler D., A fixed point formula of Lefschetz type in Arakelov geometry. I. Statement and proof. Invent. Math. 145 (2001), 333-396. MR 1872550 (2003m:14041a)

25.
Lawson H.B., Michelson M.L., Spin geometry, Princeton Univ Press, Princeton 1989.MR 1031992 (91g:53001)

26.
Ma X., Formes de torsion analytique et familles de submersions. I, Bull. Soc. Math. France 127 (1999), 541-621; II, Asian J. of Math. 4 (2000), 633-668.MR 1765553 (2001j:58059); MR 1796698 (2002e:58066)

27.
Ma X., Submersions and equivariant Quillen metrics, Ann. Inst. Fourier 50 (2000), 1539-1588. MR 1800127 (2002c:58053)

28.
Quillen D., Determinants of Cauchy-Riemann operators over a Riemann surface, Funct. Anal. Appl. 19 (1985), 31-34. MR 0783704 (86g:32035)

29.
Ray D.B., Singer I.M., Analytic torsion for complex manifolds, Ann. of Math. 98 (1973), 154-177. MR 0383463 (52:4344)

30.
Satake I., The Gauss-Bonnet theorem for $V$-manifolds, J. Math. Soc. Japon. 9 (1957), 464-492. MR 0095520 (20:2022)

31.
Taylor M., Partial Differential Equations I, II. Applied Mathematical Sciences 115, 116, Springer 1996. MR 1395148 (98b:35002b); MR 1395149 (98b:35003)


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Additional Information:

Xiaonan Ma
Affiliation: Centre de Mathématiques, UMR 7640 du CNRS, École Polytechnique, 91128 Palaiseau Cedex, France
Email: ma@math.polytechnique.fr

DOI: 10.1090/S0002-9947-05-03847-X
PII: S 0002-9947(05)03847-X
Received by editor(s): July 10, 2003
Posted: January 31, 2005
Copyright of article: Copyright 2005, American Mathematical Society


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