An analytic approach to the stratified Morse inequalities for complex cones

TL;DR

This paper provides an analytic proof that singular points of complex cones contribute only to the middle degree in stratified Morse inequalities, extending previous work on Morse theory in singular spaces.

Contribution

It offers a new analytic proof confirming the specific contribution of singular points in complex cones within stratified Morse inequalities.

Findings

Singular points contribute only to the middle degree in stratified Morse inequalities.

Analytic methods confirm known topological results for complex cones.

Extension of Morse inequalities to singular complex spaces.

Abstract

In a previous article the author extended the Witten deformation to singular spaces with cone-like singularities and to a class of Morse functions called admissible Morse functions. The method applies in particular to complex cones and stratified Morse functions in the sense of the theory developed by Goresky and MacPherson. It is well-known from stratified Morse theory that the singular points of the complex cone contribute to the stratified Morse inequalities in middle degree only. In this article an analytic proof of this fact is given.