The Witten deformation is an analytical method proposed by Witten which, given a function on a smooth compact Riemannian manifold M, leads to a proof of the Morse inequalities. In this Note we generalise the Witten deformation to singular complex algebraic curves X with cone-like singularities, and functions on X which we call admissible Morse functions. They are particular examples of stratified Morse functions in the sense of the theory developed by Goresky/MacPherson.
Soit M une variété Riemannienne compacte et soit une fonction de Morse sur M. La méthode de Witten utilise une déformation du complexe de de Rham pour démontrer les inegalités de Morse. Le but de cette Note est d'étendre cette méthode au cas des courbes algébriques complexes à singularités coniques, munis de fonctions appelées fonctions de Morse admissibles. Ces fonctions sont des fonctions de Morse stratifiées au sens de la théorie de Goresky/MacPherson.
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Ursula Ludwig 1
@article{CRMATH_2009__347_11-12_651_0, author = {Ursula Ludwig}, title = {The {Witten} complex for algebraic curves with cone-like singularities}, journal = {Comptes Rendus. Math\'ematique}, pages = {651--654}, publisher = {Elsevier}, volume = {347}, number = {11-12}, year = {2009}, doi = {10.1016/j.crma.2009.03.027}, language = {en}, }
Ursula Ludwig. The Witten complex for algebraic curves with cone-like singularities. Comptes Rendus. Mathématique, Volume 347 (2009) no. 11-12, pp. 651-654. doi : 10.1016/j.crma.2009.03.027. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.03.027/
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