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

Ursula Ludwig — 2010

Annales de l’institut Fourier

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 .

A proof of the stratified Morse inequalities for singular complex algebraic curves using the Witten deformation

Ursula Ludwig — 2011

Annales de l’institut Fourier

The Witten deformation is an analytic method proposed by Witten which, given a Morse function f : M → R on a smooth compact manifold M , allows to prove the Morse inequalities. The aim of this article is to generalise the Witten deformation to stratified Morse functions (in the sense of stratified Morse theory as developed by Goresky and MacPherson) on a singular complex algebraic curve. In a previous article the author developed the Witten deformation for the model of an algebraic curve with cone-like singularities...

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