Finitely presented groups with transcendental spectral radius
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911617263861760 |
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| author | Bodart, Corentin Osin, Denis |
| author_facet | Bodart, Corentin Osin, Denis |
| contents | We provide examples of groups with transcendental spectral radius: We first construct finitely presented examples, using links between decidability of the Word Problem and semi-computability of the spectral radius. This argument extends to the exponential growth rate and the asymptotic entropy. We also construct a finitely generated example with decidable Word Problem, using classical small-cancellation theory. Along the way, we prove that $C'(1/6)$ groups satisfy the Rapid Decay property, and deduce some properties on their spectral radii of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_17840 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Finitely presented groups with transcendental spectral radius Bodart, Corentin Osin, Denis Group Theory Logic We provide examples of groups with transcendental spectral radius: We first construct finitely presented examples, using links between decidability of the Word Problem and semi-computability of the spectral radius. This argument extends to the exponential growth rate and the asymptotic entropy. We also construct a finitely generated example with decidable Word Problem, using classical small-cancellation theory. Along the way, we prove that $C'(1/6)$ groups satisfy the Rapid Decay property, and deduce some properties on their spectral radii of independent interest. |
| title | Finitely presented groups with transcendental spectral radius |
| topic | Group Theory Logic |
| url | https://arxiv.org/abs/2404.17840 |