Comptes Rendus
no. 10
Analytic geometry/Differential topology
Scattering matrix and analytic torsion
[Matrice de diffusion et torsion analytique]

Présenté par : Jean-Michel Bismut

Martin Puchol1 ; Yeping Zhang2 ; Jialin Zhu3
1 Institut Camille-Jordan, Université Lyon-1, Bâtiment Braconnier, 43, boulevard du 11-Novembre-1918, 69622 Villeurbanne cedex, France
2 Département de mathématiques, Bâtiment 425, Faculté des sciences d'Orsay, Université Paris-Sud, 91405 Orsay cedex, France
3 Shanghai Center for Mathematical Sciences, Fudan University, Shanghai 200433, PR China
Comptes Rendus. Mathématique, Volume 355 (2017) no. 10, pp. 1089-1093.

On considère une variété compacte ayant une partie isométrique à un cylindre fini. En faisant tendre la longueur du cylindre vers l'infini, on obtient une formule asymptotique pour le déterminant du laplacien de Hodge et un développement asymptotique de la torsion L2 associée à la suite exacte de Mayer–Vietoris. On obtient une preuve analytique de la formule de recollement pour la torsion analytique.

We consider a compact manifold with a piece isometric to a (finite-length) cylinder. By making the length of the cylinder tend to infinity, we obtain an asymptotic gluing formula for the zeta determinant of the Hodge Laplacian and an asymptotic expansion of the L2 torsion of the corresponding Mayer–Vietoris exact sequence. As an application, we give a purely analytic proof of the gluing formula for analytic torsion.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2017.09.018
Martin Puchol 1 ; Yeping Zhang 2 ; Jialin Zhu 3

1 Institut Camille-Jordan, Université Lyon-1, Bâtiment Braconnier, 43, boulevard du 11-Novembre-1918, 69622 Villeurbanne cedex, France
2 Département de mathématiques, Bâtiment 425, Faculté des sciences d'Orsay, Université Paris-Sud, 91405 Orsay cedex, France
3 Shanghai Center for Mathematical Sciences, Fudan University, Shanghai 200433, PR China 
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Martin Puchol; Yeping Zhang; Jialin Zhu. Scattering matrix and analytic torsion. Comptes Rendus. Mathématique, Volume 355 (2017) no. 10, pp. 1089-1093. doi : 10.1016/j.crma.2017.09.018. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.09.018/

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