2006/10/05 by Vivien de Beauce, de Beauce, Vivien, Siddhartha Sen +1 · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Microtubule and mitosis dynamics #Topological and Geometric Data Analysis #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/0610065
39 pages, 2 figures, LOR2006
arxiv created 2006/10/05 · openalex publication_date 2006/10/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A discretisation of differential geometry using the Whitney forms of algebraic topology is consistently extended via the introduction of a pairing on the space of chains. This pairing of chains enables us to give a definition of the discrete interior product and thus provides a solution to a notorious puzzle in discretisation techniques. Further prescriptions are made to introduce metric data, as a discrete substitute for the continuum vielbein, or Cartan formulation. The original topological data of the de Rham complex is then recovered as a discrete version of the Pontryagin class, a sketch of a few examples of the technique is also provided. A map of discrete differential geometry into the non-commutative geometry of graphs is constructed which shows in a precise way the difference between them.