The geometric complex for algebraic curves with cone-like singularities and admissible Morse functions

Ludwig, Ursula

Annales de l'Institut Fourier, Tome 60 (2010) no. 5, pp. 1533-1560.

Dans une note précédente, l’auteur a donné une généralisation de la preuve de Witten des inégalités 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 des petites valeurs propres à l’aide d’un sous-complexe approprié du complexe des cellules instables.

In a previous note the author gave a generalisation of Witten’s proof of the Morse inequalities to the model of a complex singular 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 $f$.

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