Finiteness of rank invariants of multidimensional persistent homology groups
@article{Cagliari2011FinitenessOR, title={Finiteness of rank invariants of multidimensional persistent homology groups}, author={F. Cagliari and C. Landi}, journal={ArXiv}, year={2011}, volume={abs/1001.0358} }
Rank invariants are a parametrized version of Betti numbers of a space multi-filtered by a continuous vector-valued function. In this note we give a sufficient condition for their finiteness. This condition is sharp for spaces embeddable in R^n.
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