Singular (Lipschitz) homology and homology of integral currents

2009/02/23 by Christian Riedweg, Riedweg, Christian, Daniel Schäppi +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG) #math.DG #math.MG

paper · pdf · doi:10.48550/arxiv.0902.3831

20 pages, 1 figure

arxiv created 2009/02/23 · arxiv updated 2009/12/01

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).

Related

• The coincidence of the homologies of integral currents and of integral singular chains, via cosheaves
• The coincidence of the current homology and the measure homology via a new topology on spaces of Lipschitz maps
• Homology by metric currents
• Homology Classes of Semi-Algebraic Sets and Mass Minimization
• Lipschitz Chain Approximation of Metric Integral Currents