Stability of L2-Invariants on Stratified Spaces

Let M̄ be a compact smoothly stratified pseudo-manifold endowed with a wedge metric g. Let M̄Γ be a Galois Γ-covering. Under additional assumptions on M̄, satisfied for example by Witt pseudo-manifolds, we show that the L²-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.