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- W4287100767 abstract "Bonamy et al cite{BBEGLPS} showed that graphs of polynomial growth have finite asymptotic dimension. We refine their result showing that a graph of polynomial growth strictly less than $n^{k+1}$ has asymptotic dimension at most $k$. As a corollary Riemannian manifolds of bounded geometry and polynomial growth strictly less than $n^{k+1}$ have asymptotic dimension at most $k$. We show also that there are graphs of growth $<n^{1+epsilon}$ for any $epsilon >0$ and infinite asymptotic Assouad-Nagata dimension." @default.
- W4287100767 created "2022-07-25" @default.
- W4287100767 creator A5073268569 @default.
- W4287100767 date "2021-07-05" @default.
- W4287100767 modified "2023-10-16" @default.
- W4287100767 title "Polynomial growth and asymptotic dimension" @default.
- W4287100767 doi "https://doi.org/10.48550/arxiv.2107.01972" @default.
- W4287100767 hasPublicationYear "2021" @default.
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