Singular (Lipschitz) homology and homology of integral currents

Details Singular (Lipschitz) homology and homology of integral currents Singular (Lipschitz) homology and homology of integral currents

2009-02-23

arxiv.org/abs/0902.3831v1

Mathematics

Differential Geometry

20 pages, 1 figure

Scientific paper

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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