Topological Data Analysis uses homology as a feature for large data sets. It has successfully addressed the issue of the robustness of computing homology. Nevertheless, the conditioning number suggests an alternative approach. When computing the cohomology of a graph (or a simplicial complex), it has geometric significance: it is known as Cheeger's constant or spectral gap. This indicates that (co-)chain complexes contain more information than their mere (co-)homology. We turn the set of normed chain complexes into a metric space and study a compactness criterion.
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Passcode: A group is called an ________ group if it admits an invariant mean. (8 letters, lowercase)