no. 9-10
Differential Geometry
Comparison between two complexes on a singular space
[Comparaison entre deux complexes sur un espace singulier]

Présenté par : Jean-Michel Bismut

Ludwig, Ursula1
1 Mathematisches Institut, Eckerstrasse 1, 79104 Freiburg, Germany
Comptes Rendus. Mathématique, Tome 350 (2012) no. 9-10, pp. 525-528.

Cette Note a deux buts : Dans une première partie on étend la déformation de Witten au cas dʼun espace stratifié X muni de fonctions appelées fonctions de Morse radiales. On démontre le théorème du trou spectral pour le laplacien de Witten. Dans la deuxième partie, on se place dans la situation dʼun espace à singularités isolées et on construit un complexe géométrique que lʼon compare à celui des petites valeurs propres.

The aim of this Note is twofold. In the first step we study the Witten deformation for stratified spaces X and radial Morse functions on them and prove a spectral gap theorem for the Witten Laplacian. In the second step we focus on spaces with isolated conic singularities, where we construct a geometric complex associated to the Morse function and give two comparison results.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2012.05.014
Ludwig, Ursula 1

1 Mathematisches Institut, Eckerstrasse 1, 79104 Freiburg, Germany 
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Ludwig, Ursula. Comparison between two complexes on a singular space. Comptes Rendus. Mathématique, Tome 350 (2012) no. 9-10, pp. 525-528. doi : 10.1016/j.crma.2012.05.014. http://www.numdam.org/articles/10.1016/j.crma.2012.05.014/

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