A subset of Euclidean space with large Vietoris-Rips homology
Jean-Marie Droz · arXiv (Cornell University) · 2012
We construct a compact subset K of the four dimensional Euclidean space with the following property: For all values of the parameter in an interval, the Vietoris-Rips complex of K has uncountably generated first homology. This answers a question that arose in work on persistent homology.