Homology by metric currents

2013/04/23 by Samuele Mongodi, Mongodi, Samuele
Mathematics · #30L99 #550N40 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #Metric Geometry (math.MG) #math.AT #math.MG #msc:30L99 #msc:550N40

paper · pdf · doi:10.48550/arxiv.1304.6205

7 pages

openalex publication_date 2013/04/23 · arxiv created 2013/09/23 · arxiv updated 2013/09/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• The coincidence of the homologies of integral currents and of integral singular chains, via cosheaves
• Singular (Lipschitz) homology and homology of integral currents
• The coincidence of the current homology and the measure homology via a new topology on spaces of Lipschitz maps
• Application of metric currents to complex analysis
• Metric currents, differentiable structures, and Carnot groups