$L^2$-Betti numbers of Dehn fillings
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916591641296896 |
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| author | Petrosyan, Nansen Sun, Bin |
| author_facet | Petrosyan, Nansen Sun, Bin |
| contents | We initiate the study of the $L^2$-Betti numbers of group-theoretic Dehn fillings. For a broad class of virtually special groups $G$, we prove that the $L^2$-Betti numbers of sufficiently deep Dehn fillings $\overline{G}$ are equal to those of $G$. As applications, we verify the Singer Conjecture for certain Einstein manifolds, establish a virtual fibering criterion for $\overline{G}$, obtain bounds on deficiency of $\overline{G}$, and provide new examples of hyperbolic groups with exotic subgroups that arise as Dehn fillings of any cusped arithmetic hyperbolic manifold of dimension at least four. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_16090 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $L^2$-Betti numbers of Dehn fillings Petrosyan, Nansen Sun, Bin Group Theory Algebraic Topology Differential Geometry Geometric Topology 20F65 We initiate the study of the $L^2$-Betti numbers of group-theoretic Dehn fillings. For a broad class of virtually special groups $G$, we prove that the $L^2$-Betti numbers of sufficiently deep Dehn fillings $\overline{G}$ are equal to those of $G$. As applications, we verify the Singer Conjecture for certain Einstein manifolds, establish a virtual fibering criterion for $\overline{G}$, obtain bounds on deficiency of $\overline{G}$, and provide new examples of hyperbolic groups with exotic subgroups that arise as Dehn fillings of any cusped arithmetic hyperbolic manifold of dimension at least four. |
| title | $L^2$-Betti numbers of Dehn fillings |
| topic | Group Theory Algebraic Topology Differential Geometry Geometric Topology 20F65 |
| url | https://arxiv.org/abs/2412.16090 |