Comptes Rendus
Differential Geometry
The geometric complex for algebraic curves with cone-like singularities and admissible Morse functions
Comptes Rendus. Mathématique, Volume 347 (2009) no. 13-14, pp. 801-804.

In a previous Note the author gave a generalisation of Witten's proof of the Morse inequalities to the model of a singular complex algebraic curve X and a stratified Morse function f. In this Note a geometric interpretation of the complex of eigenforms of the Witten Laplacian corresponding to small eigenvalues is provided in terms of an appropriate subcomplex of the complex of unstable cells of critical points of f.

Dans une Note précédente, l'auteur a donné une généralisation de la preuve de Witten des inegalités de Morse pour le cas modèle d'une courbe algébrique complexe singulière et d'une fonction de Morse stratifiée. Le but de cette Note est de donner une interprétation géométrique du complexe des formes propres du Laplacien de Witten pour de petites valeurs propres à l'aide d'un sous-complexe approprié du complexe des cellules instables.

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Published online:
DOI: 10.1016/j.crma.2009.03.028

Ursula Ludwig 1

1 Mathematisches Institut, Eckerstrasse 1, 79104 Freiburg, Germany
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Ursula Ludwig. The geometric complex for algebraic curves with cone-like singularities and admissible Morse functions. Comptes Rendus. Mathématique, Volume 347 (2009) no. 13-14, pp. 801-804. doi : 10.1016/j.crma.2009.03.028. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.03.028/

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[2] M. Goresky; R. MacPherson Stratified Morse Theory, Ergebnisse der Mathematik und ihrer Grenzgebiete (3), Results in Mathematics and Related Areas (3), vol. 14, Springer-Verlag, Berlin, 1988

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[5] U. Ludwig The Witten complex for algebraic curves with cone-like singularities, C. R. Acad. Sci. Paris, Ser. I, Volume 347 (2009) no. 11–12, pp. 651-654

[6] E. Witten Supersymmetry and Morse theory, J. Differential Geom., Volume 17 (1982) no. 4, pp. 661-692

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