Free groups are $L^2$-subgroup rigid
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917245956915200 |
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| author | Jaikin-Zapirain, Andrei |
| author_facet | Jaikin-Zapirain, Andrei |
| contents | In this paper, we introduce the notion of $L^2$-subgroup rigid groups and demonstrate that free groups are $L^2$-subgroup rigid. As a consequence, we establish the equivalence between compressibility, inertness, strong inertness, and $L^2$-independence for a finitely generated subgroup of a free group, confirming a conjecture by Dicks and Ventura as well as the one by Antolin and Jaikin-Zapirain. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_09515 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Free groups are $L^2$-subgroup rigid Jaikin-Zapirain, Andrei Group Theory In this paper, we introduce the notion of $L^2$-subgroup rigid groups and demonstrate that free groups are $L^2$-subgroup rigid. As a consequence, we establish the equivalence between compressibility, inertness, strong inertness, and $L^2$-independence for a finitely generated subgroup of a free group, confirming a conjecture by Dicks and Ventura as well as the one by Antolin and Jaikin-Zapirain. |
| title | Free groups are $L^2$-subgroup rigid |
| topic | Group Theory |
| url | https://arxiv.org/abs/2403.09515 |