Dans cette Note, on utilise la théorie des opérateurs de Toeplitz pour calculer le terme dominant dans lʼasymptotique quand des formes de torsion analytique associées à une famille de fibrés plats, qui sont eux-mêmes des images directes de , où L est un fibré en droites positif le long des fibres dʼune fibration plate en variétés de Kähler. Le terme dominant est obtenu par intégration de formes différentielles calculables localement.
In this Note, we use the theory of Toeplitz operators to obtain the leading term in the asymptotic expansion of the analytic torsion forms associated with a family of flat vector bundles that are the direct image of , where L is a positive line bundle along the fibres of a flat fibration by compact Kähler manifolds. The leading term is given by the integral of locally computable differential forms.
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@article{CRMATH_2011__349_17-18_977_0,
author = {Bismut, Jean-Michel and Ma, Xiaonan and Zhang, Weiping},
title = {Op\'erateurs de {Toeplitz} et torsion analytique asymptotique},
journal = {Comptes Rendus. Math\'ematique},
pages = {977--981},
publisher = {Elsevier},
volume = {349},
number = {17-18},
year = {2011},
doi = {10.1016/j.crma.2011.08.010},
language = {fr},
url = {http://www.numdam.org/articles/10.1016/j.crma.2011.08.010/}
}
TY - JOUR AU - Bismut, Jean-Michel AU - Ma, Xiaonan AU - Zhang, Weiping TI - Opérateurs de Toeplitz et torsion analytique asymptotique JO - Comptes Rendus. Mathématique PY - 2011 SP - 977 EP - 981 VL - 349 IS - 17-18 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2011.08.010/ DO - 10.1016/j.crma.2011.08.010 LA - fr ID - CRMATH_2011__349_17-18_977_0 ER -
%0 Journal Article %A Bismut, Jean-Michel %A Ma, Xiaonan %A Zhang, Weiping %T Opérateurs de Toeplitz et torsion analytique asymptotique %J Comptes Rendus. Mathématique %D 2011 %P 977-981 %V 349 %N 17-18 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2011.08.010/ %R 10.1016/j.crma.2011.08.010 %G fr %F CRMATH_2011__349_17-18_977_0
Bismut, Jean-Michel; Ma, Xiaonan; Zhang, Weiping. Opérateurs de Toeplitz et torsion analytique asymptotique. Comptes Rendus. Mathématique, Tome 349 (2011) no. 17-18, pp. 977-981. doi : 10.1016/j.crma.2011.08.010. http://www.numdam.org/articles/10.1016/j.crma.2011.08.010/
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