Asian Journal of Mathematics

Volume 21 (2017)

Number 1

Witten’s perturbation on strata

Pages: 47 – 126



Jesús A. Álvarez López (Departamento de Xeometría e Topoloxía, Facultade de Matemáticas, Universidade de Santiago de Compostela, Spain)

Manuel Calaza (Research Lab 10 and Rheumatology Unit, Hospital Clinico Universitario de Santiago de Compostela, Spain)


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, equipped with adapted metrics. An adaptation of the analytic method of Witten is used in the proof, as well as certain operator related with the Dunkl harmonic oscillator.


Morse inequalities, ideal boundary condition, Thom–Mather stratification, Witten’s perturbation

2010 Mathematics Subject Classification

32S60, 58A14

Published 16 March 2017