A complex in Morse theory computing intersection homology
Annales de l'Institut Fourier, Volume 67 (2017) no. 1, pp. 197-236.

Let X be a space with isolated conical singularities. The aim of this article is to establish, using anti-radial Morse functions on X, a combinatorial complex which computes the intersection homology of X. 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 X. 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.

Dans cet article on associe à une fonction de Morse f anti-radiale sur un espace singulier X à singularités coniques un complexe généré par les points critiques de f 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.

Published online:
DOI: 10.5802/aif.3079
Classification: 55N33,  58A35,  58K05,  57R70
Keywords: intersection homology, Morse theory, radial vector fields, Thom-Smale complex
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     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},
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     doi = {10.5802/aif.3079},
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Ludwig, Ursula. A complex in Morse theory computing intersection homology. Annales de l'Institut Fourier, Volume 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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