Persistent Homology and the Upper Box Dimension.
We introduce a fractal dimension for a metric space based on the persistent homology of subsets of that space. We exhibit hypotheses under which this dimension is comparable to the upper box dimension; in particular, the dimensions coincide for subsets of $\mathbb{R}^2$ whose upper box dimension exceeds $1.5.$
Publisher URL: http://arxiv.org/abs/1802.00533
DOI: arXiv:1802.00533v1
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