Triviality of $K$-homology classes of Euler characteristic operators of stratified pseudomanifolds

We show that the $K$-homology classes of the Euler characteristic operators associated with the minimal and maximal ideal boundary conditions of the de Rham differential on the regular part of a connected compact Thom-Mather stratified pseudomanifold, equipped with an adapted metric, are trivial beyond their indices. These indices are the Euler characteristics of the corresponding $L^2$-cohomologies. This generalizes a result of J. Rosenberg for manifolds. The proof uses Witten deformation of the de Rham operator associated with a stratified Morse function, following the work of Álvarez López and Calaza.