Singular (Lipschitz) homology and homology of integral currents

Abstract

We compare the homology groups $H_n^{IC}(X)$ of the chain complex of integral currents with compact support of a metric space $X$ with the singular Lipschitz homology $H_n^L(X)$ and with ordinary singular homology. If $X$ satisfies certain cone inequalities all these homology theories coincide. On the other hand, for the Hawaiian Earring the homology of integral currents differs from the singular Lipschitz homology and it differs also from the classical singular homology $H_n(X)$.

arXiv comment20 pages, 1 figure

Cited by in corpus (5)

• The coincidence of the homologies of integral currents and of integral singular chains, via cosheaves
• Homology by metric currents
• Some results on maps that factor through a tree
• Higher rank hyperbolicity
• The coincidence of the current homology and the measure homology via a new topology on spaces of Lipschitz maps