Singular (Lipschitz) homology and homology of integral currents

Christian Riedweg; Daniel Schäppi

Singular (Lipschitz) homology and homology of integral currents

Differential Geometry 2009-02-24 v1 Metric Geometry

Authors: Christian Riedweg , Daniel Schäppi

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 $H_n(X)$ .

Keywords

integral currents singular Lipschitz homology singular homology cone inequalities Hawaiian Earring

Cite

@article{arxiv.0902.3831,
  title  = {Singular (Lipschitz) homology and homology of integral currents},
  author = {Christian Riedweg and Daniel Schäppi},
  journal= {arXiv preprint arXiv:0902.3831},
  year   = {2009}
}

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20 pages, 1 figure

Singular (Lipschitz) homology and homology of integral currents

Abstract

Keywords

Cite

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