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Singular (Lipschitz) homology and homology of integral currents

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arxiv 0902.3831 v1 pith:2OYTPUDI submitted 2009-02-23 math.DG math.MG

Christian Riedweg , Daniel Schäppi This is my paper · ORCID
classification math.DGmath.MG
keywords homologysingularcurrentsintegrallipschitzdifferscertainchain
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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 $H^L_n (X)$ 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 $H_n(X)$.

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