Polynomial growth and asymptotic dimension
Bonamy et al. [4] showed that graphs of polynomial growth have finite asymptotic dimension. We refine their result showing that a graph of polynomial growth strictly less than nk+1 has asymptotic dimension at most k. As a corollary Riemannian manifolds of bounded geometry and polynomial growth stric...
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| Format: | Journal article |
| Language: | English |
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Springer Nature
2023
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| Summary: | Bonamy et al. [4] showed that graphs of polynomial growth have finite asymptotic dimension. We refine their result showing that a graph of polynomial growth strictly less than nk+1 has asymptotic dimension at most k. As a corollary Riemannian manifolds of bounded geometry and polynomial growth strictly less than nk+1 have asymptotic dimension at most k.
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We show also that there are graphs of growth < n1+ϵ for any ϵ > 0 and infinite asymptotic Assouad—Nagata dimension. |
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