An $\ell^2$ Obstruction for Elementary Embeddings of Hyperbolic Groups
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866917514268639232 |
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| author | MacMahon, Connor |
| author_facet | MacMahon, Connor |
| contents | The first $\ell^2$ Betti number of a group is non-decreasing under various embeddings arising from first order logic. Strict inequality is proved for elementary embeddings of non-abelian proper subgroups within torsion free hyperbolic groups using Perin's classification of such inclusions. The monotonicity is further demonstrated for existential embeddings of arbitrary finitely generated groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_20397 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An $\ell^2$ Obstruction for Elementary Embeddings of Hyperbolic Groups MacMahon, Connor Group Theory Logic Operator Algebras The first $\ell^2$ Betti number of a group is non-decreasing under various embeddings arising from first order logic. Strict inequality is proved for elementary embeddings of non-abelian proper subgroups within torsion free hyperbolic groups using Perin's classification of such inclusions. The monotonicity is further demonstrated for existential embeddings of arbitrary finitely generated groups. |
| title | An $\ell^2$ Obstruction for Elementary Embeddings of Hyperbolic Groups |
| topic | Group Theory Logic Operator Algebras |
| url | https://arxiv.org/abs/2605.20397 |