Let M be a compact smoothly stratified pseudo-manifold endowed with a wedge metric. Let M_G be a Galois-covering. Under additional assumptions on M, 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.
Stability of L2-Invariants on Stratified Spaces / Bei, Francesco; Piazza, Paolo; Vertman, Boris. - In: INTERNATIONAL MATHEMATICS RESEARCH NOTICES. - ISSN 1073-7928. - 2024:21(2024), pp. 13695-13723. [10.1093/imrn/rnae214]
Stability of L2-Invariants on Stratified Spaces
Bei, Francesco
;Piazza, Paolo;
2024
Abstract
Let M be a compact smoothly stratified pseudo-manifold endowed with a wedge metric. Let M_G be a Galois-covering. Under additional assumptions on M, 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.| File | Dimensione | Formato | |
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