Asymptotic invariants of residually finite just infinite groups
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913618857033728 |
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| author | Jaikin-Zapirain, Andrei Kionke, Steffen |
| author_facet | Jaikin-Zapirain, Andrei Kionke, Steffen |
| contents | Recently, Eduard Schesler and the second author constructed examples of finitely generated residually finite, hereditarily just infinite groups with positive first $L^2$-Betti number. In contrast to their result, we show that a finitely generated residually-$p$ just infinite group has trivial first $L^2$-Betti number. Moreover, we prove that the normal homology rank gradient of a finitely generated, residually finite, just infinite group vanishes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_14765 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Asymptotic invariants of residually finite just infinite groups Jaikin-Zapirain, Andrei Kionke, Steffen Group Theory Recently, Eduard Schesler and the second author constructed examples of finitely generated residually finite, hereditarily just infinite groups with positive first $L^2$-Betti number. In contrast to their result, we show that a finitely generated residually-$p$ just infinite group has trivial first $L^2$-Betti number. Moreover, we prove that the normal homology rank gradient of a finitely generated, residually finite, just infinite group vanishes. |
| title | Asymptotic invariants of residually finite just infinite groups |
| topic | Group Theory |
| url | https://arxiv.org/abs/2412.14765 |