[Un complexe en théorie de Morse qui calcule l’homologie d’intersection]
Dans cet article on associe à une fonction de Morse anti-radiale sur un espace singulier à singularités coniques un complexe généré par les points critiques de et par certaines formes sur le link de la singularité. Ce complexe calcule de façon canonique l’homologie d’intersection. Également on discute le comportement de ce complexe par rapport aux homotopies. Le complexe construit dans cet article est un analogue du complexe de Thom-Smale sur une variété lisse pour une fonction de Morse lisse et l’homologie singulière.
Let be a space with isolated conical singularities. The aim of this article is to establish, using anti-radial Morse functions on , a combinatorial complex which computes the intersection homology of . The complex constructed here, is generated by the smooth critical points of the Morse function and representatives of the de Rham cohomology (in low degree) of the link manifolds of the singularities of . It can be seen as an analogue of the famous Thom-Smale complex for smooth Morse functions and singular homology on a compact manifold. The article also discusses the homotopy principle familiar in smooth Morse homology in this singular context.
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Keywords: intersection homology, Morse theory, radial vector fields, Thom-Smale complex
Mot clés : homologie d’intersection, théorie de Morse, champs radiaux, complexe de Thom-Smale
Ludwig, Ursula 1
CC-BY-ND 4.0
@article{AIF_2017__67_1_197_0,
author = {Ludwig, Ursula},
title = {A complex in {Morse} theory computing intersection homology},
journal = {Annales de l'Institut Fourier},
pages = {197--236},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {67},
number = {1},
year = {2017},
doi = {10.5802/aif.3079},
language = {en},
url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3079/}
}
TY - JOUR AU - Ludwig, Ursula TI - A complex in Morse theory computing intersection homology JO - Annales de l'Institut Fourier PY - 2017 SP - 197 EP - 236 VL - 67 IS - 1 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3079/ DO - 10.5802/aif.3079 LA - en ID - AIF_2017__67_1_197_0 ER -
%0 Journal Article %A Ludwig, Ursula %T A complex in Morse theory computing intersection homology %J Annales de l'Institut Fourier %D 2017 %P 197-236 %V 67 %N 1 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3079/ %R 10.5802/aif.3079 %G en %F AIF_2017__67_1_197_0
Ludwig, Ursula. A complex in Morse theory computing intersection homology. Annales de l'Institut Fourier, Tome 67 (2017) no. 1, pp. 197-236. doi : 10.5802/aif.3079. https://aif.centre-mersenne.org/articles/10.5802/aif.3079/
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