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Comptes Rendus Mathématique
Volume 350, n° 9-10
pages 525-528 (mai 2012)
Doi : 10.1016/j.crma.2012.05.014
Received : 20 May 2011 ;  accepted : 26 May 2012
Comparison between two complexes on a singular space
Comparaison entre deux complexes sur un espace singulier
 

Ursula Ludwig
Mathematisches Institut, Eckerstrasse 1, 79104 Freiburg, Germany 

Abstract

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.

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Résumé

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.

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© 2012  Published by Elsevier Masson SAS de la part de Académie des sciences.
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