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

Ursula Ludwig

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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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