Metric criteria for fixed price of countable groups
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916993270022144 |
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| author | Bevilacqua, Erin Bowen, Lewis |
| author_facet | Bevilacqua, Erin Bowen, Lewis |
| contents | We establish general criteria for a countable group $Γ$ to have fixed price 1 depending on a choice of left-invariant proper metric on $Γ$. We apply this criterion to show that if $Γ_1,Γ_2$ are two countable groups satisfying a certain growth condition then $Γ_1\times Γ_2$ has fixed price 1. For example, $Γ\times Γ$ has fixed price 1 for any countable group $Γ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_05459 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Metric criteria for fixed price of countable groups Bevilacqua, Erin Bowen, Lewis Group Theory Dynamical Systems We establish general criteria for a countable group $Γ$ to have fixed price 1 depending on a choice of left-invariant proper metric on $Γ$. We apply this criterion to show that if $Γ_1,Γ_2$ are two countable groups satisfying a certain growth condition then $Γ_1\times Γ_2$ has fixed price 1. For example, $Γ\times Γ$ has fixed price 1 for any countable group $Γ$. |
| title | Metric criteria for fixed price of countable groups |
| topic | Group Theory Dynamical Systems |
| url | https://arxiv.org/abs/2510.05459 |