A proof of the stratified Morse inequalities for singular complex algebraic curves using the Witten deformation (Q416003)

The main purpose of this paper is to generalize the Witten deformation in the framework of stratified Morse functions on a singular algebraic curve. The author establishes that stratified Morse functions in the sense of the theory developed by Goresky and MacPherson are admissible. Also a local model for the Witten Laplace operator near singular points is developed and a local version of the spectral gap theorem is proved. The Agmon-type estimates, used to prove the exponential decay of the eigenforms of the model operator, are established in the final part of the paper.