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.
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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@article{CRMATH_2012__350_9-10_525_0,
author = {Ludwig, Ursula},
title = {Comparison between two complexes on a singular space},
journal = {Comptes Rendus. Math\'ematique},
pages = {525--528},
publisher = {Elsevier},
volume = {350},
number = {9-10},
year = {2012},
doi = {10.1016/j.crma.2012.05.014},
language = {en},
url = {https://www.numdam.org/articles/10.1016/j.crma.2012.05.014/}
}
TY - JOUR AU - Ludwig, Ursula TI - Comparison between two complexes on a singular space JO - Comptes Rendus. Mathématique PY - 2012 SP - 525 EP - 528 VL - 350 IS - 9-10 PB - Elsevier UR - https://www.numdam.org/articles/10.1016/j.crma.2012.05.014/ DO - 10.1016/j.crma.2012.05.014 LA - en ID - CRMATH_2012__350_9-10_525_0 ER -
%0 Journal Article %A Ludwig, Ursula %T Comparison between two complexes on a singular space %J Comptes Rendus. Mathématique %D 2012 %P 525-528 %V 350 %N 9-10 %I Elsevier %U https://www.numdam.org/articles/10.1016/j.crma.2012.05.014/ %R 10.1016/j.crma.2012.05.014 %G en %F CRMATH_2012__350_9-10_525_0
Ludwig, Ursula. Comparison between two complexes on a singular space. Comptes Rendus. Mathématique, Volume 350 (2012) no. 9-10, pp. 525-528. doi : 10.1016/j.crma.2012.05.014. https://www.numdam.org/articles/10.1016/j.crma.2012.05.014/
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