Homology by metric currents

Abstract

Metric currents are, in a certain sense, a metric analogous of flat currents, therefore are related to the geometry of the space and of their support. In this short note, we try to give some evidence for the previous statement, by showing that the homology which can be defined by means of metric normal currents coincides, on nice enough metric spaces, with the usual singular homology.

7 pages

References in corpus (2)

• Singular (Lipschitz) homology and homology of integral currents
• The coincidence of the homologies of integral currents and of integral singular chains, via cosheaves

Cited by in corpus (3)

• The coincidence of the homologies of integral currents and of integral singular chains, via cosheaves
• Orientability and fundamental classes of Alexandrov spaces with applications
• The coincidence of the current homology and the measure homology via a new topology on spaces of Lipschitz maps