[Formules d'anomalie pour les métriques de Ray–Singer sur les variétés à bord]
On annonce une formule d'anomalie pour les métriques de Ray–Singer d'un fibré plat F sur une variété à bord X . On ne suppose ni que la métrique sur F est plate, ni que la métrique sur X a une structure produit près du bord.
We establish an anomaly formula for Ray–Singer metrics defined by a Hermitian metric on a flat vector bundle over a Riemannian manifold with boundary. We do not assume that the Hermitian metric on the flat vector bundle is flat, nor that the Riemannian metric has product structure near the boundary.
Accepté le :
Publié le :
Jochen Brüning 1 ; Xiaonan Ma 2
@article{CRMATH_2002__335_7_603_0,
author = {Jochen Br\"uning and Xiaonan Ma},
title = {An anomaly formula for {Ray{\textendash}Singer} metrics on manifolds with boundary},
journal = {Comptes Rendus. Math\'ematique},
pages = {603--608},
publisher = {Elsevier},
volume = {335},
number = {7},
year = {2002},
doi = {10.1016/S1631-073X(02)02496-2},
language = {en},
}
Jochen Brüning; Xiaonan Ma. An anomaly formula for Ray–Singer metrics on manifolds with boundary. Comptes Rendus. Mathématique, Volume 335 (2002) no. 7, pp. 603-608. doi : 10.1016/S1631-073X(02)02496-2. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02496-2/
[1] Complex immersions and Quillen metrics, Publ. Math. IHES, Volume 74 (1991), pp. 1-297
[2] An Extension of a Theorem by Cheeger and Müller, Astérisque, 205, 1992
[3] Milnor and Ray–Singer metrics on the equivariant determinant of a flat vector bundle, Geom. Funct. Anal., Volume 4 (1994), pp. 136-212
[4] Differential Forms in Algebraic Topology, Graduate Texts in Math., 82, Springer, New York, 1982
[5] J. Brüning, X. Ma, An anomaly formula for Ray–Singer metrics on manifolds with boundary, to appear
[6] Analytic torsion and the heat equation, Ann of Math., Volume 109 (1979), pp. 259-322
[7] On the curvatura integra in a Riemannian manifold, Ann. of Math., Volume 46 (1945), pp. 674-684
[8] Analytic torsion and R-torsion for manifolds with boundary, Asian J. Math., Volume 4 (2000), pp. 695-714
[9] Analytic torsion for group actions, J. Differential Geom., Volume 34 (1991), pp. 431-481
[10] Analytic and topological torsion for manifolds with boundary and symmetry, J. Differential Geom., Volume 37 (1993), pp. 263-322
[11] Superconnections, Thom classes, and equivariant differential forms, Topology, Volume 25 (1986), pp. 85-110
[12] Analytic torsion and R-torsion of Riemannian manifolds, Adv. in Math., Volume 28 (1978), pp. 233-305
[13] Analytic torsion and R-torsion for unimodular representations, J. Amer. Math. Soc., Volume 6 (1993), pp. 721-753
[14] R-torsion and the Laplacian on Riemannian manifolds, Adv. in Math., Volume 7 (1971), pp. 145-210
Cité par Sources :
Commentaires - Politique