Stability of L 2-Invariants on Stratified Spaces

Let $\overline{M}$ be a compact smoothly stratified pseudo-manifold endowed with a wedge metric $g$. Let $\overline{M}_{\Gamma }$ be a Galois $\Gamma $-covering. Under additional assumptions on $\overline{M}$, satisfied for example by Witt pseudo-manifolds, we show that the $L^{2}$-Betti numbers and the Novikov–Shubin invariants are well defined. We then establish their invariance under a smoothly stratified codimension-preserving homotopy equivalence, thus extending results of Dodziuk, Gromov, and Shubin to these pseudo-manifolds.