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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2310.05721 |
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| _version_ | 1866929495348346880 |
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| author | Bei, Francesco Piazza, Paolo Vertman, Boris |
| author_facet | Bei, Francesco Piazza, Paolo Vertman, Boris |
| contents | Let $\overline{M}$ be a compact smoothly stratified pseudo-manifold endowed with a wedge metric $g$. Let $\overline{M}_Γ$ be a Galois $Γ$-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, strongly stratum preserving homotopy equivalence, thus extending results of Dodziuk, Gromov and Shubin to these pseudo-manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_05721 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Stability of $L^2-$invariants on stratified spaces Bei, Francesco Piazza, Paolo Vertman, Boris Differential Geometry Geometric Topology 58A12, 58G12, 58A14 Let $\overline{M}$ be a compact smoothly stratified pseudo-manifold endowed with a wedge metric $g$. Let $\overline{M}_Γ$ be a Galois $Γ$-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, strongly stratum preserving homotopy equivalence, thus extending results of Dodziuk, Gromov and Shubin to these pseudo-manifolds. |
| title | Stability of $L^2-$invariants on stratified spaces |
| topic | Differential Geometry Geometric Topology 58A12, 58G12, 58A14 |
| url | https://arxiv.org/abs/2310.05721 |