Witten's perturbation on strata
Jes\'us A. \'Alvarez L\'opez, Manuel Calaza
TL;DR
This paper extends Morse inequalities to stratified spaces with boundary conditions, using Witten's perturbation method and Dunkl harmonic oscillator techniques.
Contribution
It introduces a Morse inequality framework for de Rham complexes on stratified spaces with adapted metrics, employing Witten's analytic approach.
Findings
Morse inequalities established for stratified spaces with boundary conditions
Application of Witten's perturbation method in a stratified setting
Use of Dunkl harmonic oscillator perturbations in the proof
Abstract
The main result is a version of Morse inequalities for the minimum and maximum ideal boundary conditions of the de Rham complex on strata of compact Thom-Mather stratifications, endowed with adapted metrics. An adaptation of the analytic method of Witten is used in the proof, as well as certain perturbation of the harmonic oscillator related with the Dunkl harmonic oscillator.
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