Stability of $L^2-$invariants on stratified spaces
| Autor: | Bei, Francesco, Piazza, Paolo, Vertman, Boris |
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| Rok vydání: | 2023 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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, strongly stratum preserving homotopy equivalence, thus extending results of Dodziuk, Gromov and Shubin to these pseudo-manifolds. Comment: 33 pages, proof of Lemma 4.10 and Theorem 4.11 clarified, Corollary 5.3 improved |
| Databáze: | arXiv |
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