[Un théorème de l'indice pour la caractéristique d'Euler d'intersection d'un cône infini]
Le but de cette note est d'établir un théorème de l'indice pour la caractéristique d'Euler d'intersection d'un cône. Dans un premier temps, on étudie les propriétés spectrales du laplacien de Witten et on établit une formule de McKean–Singer. On donne aussi une formule explicite pour la fonction zêta associée au laplacien de Witten. Dans une deuxième partie, on applique des techniques d'indice local au laplacien de Witten. On obtient une formule qui exprime la caractéristique d'Euler d'intersection du cône comme la somme de deux termes, l'un local, l'autre étant l'invariant de Cheeger.
The aim of this note is to establish an index formula for the intersection Euler characteristic of a cone. The main actor of these notes is the model Witten Laplacian on the infinite cone. First, we study its spectral properties and establish a McKean–Singer-type formula. We also give an explicit formula for the zeta function of the model Witten Laplacian. In a second step, we apply local index techniques to the model Witten Laplacian. By combining these two steps, we express the absolute and relative intersection Euler characteristic of the cone as a sum of two terms, a term which is local, and a second term which is the Cheeger invariant.
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@article{CRMATH_2017__355_1_94_0,
author = {Ludwig, Ursula},
title = {An index formula for the intersection {Euler} characteristic of an infinite cone},
journal = {Comptes Rendus. Math\'ematique},
pages = {94--98},
publisher = {Elsevier},
volume = {355},
number = {1},
year = {2017},
doi = {10.1016/j.crma.2016.11.003},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2016.11.003/}
}
TY - JOUR AU - Ludwig, Ursula TI - An index formula for the intersection Euler characteristic of an infinite cone JO - Comptes Rendus. Mathématique PY - 2017 SP - 94 EP - 98 VL - 355 IS - 1 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2016.11.003/ DO - 10.1016/j.crma.2016.11.003 LA - en ID - CRMATH_2017__355_1_94_0 ER -
%0 Journal Article %A Ludwig, Ursula %T An index formula for the intersection Euler characteristic of an infinite cone %J Comptes Rendus. Mathématique %D 2017 %P 94-98 %V 355 %N 1 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2016.11.003/ %R 10.1016/j.crma.2016.11.003 %G en %F CRMATH_2017__355_1_94_0
Ludwig, Ursula. An index formula for the intersection Euler characteristic of an infinite cone. Comptes Rendus. Mathématique, Tome 355 (2017) no. 1, pp. 94-98. doi : 10.1016/j.crma.2016.11.003. http://www.numdam.org/articles/10.1016/j.crma.2016.11.003/
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