Discretising differential geometry via a new product on the space of chains
| dc.creator | de Beauce, Vivien | |
| dc.creator | Sen, Siddhartha | |
| dc.date | 2006-10-05 | |
| dc.date.accessioned | 2026-07-07T07:28:21Z | |
| dc.date.available | 2026-07-07T07:28:21Z | |
| dc.description | 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. | |
| dc.description | 39 pages, 2 figures, LOR2006 | |
| dc.identifier | https://arxiv.org/abs/hep-th/0610065 | |
| dc.identifier | http://arxiv.org/abs/hep-th/0610065 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/117704 | |
| dc.subject | High Energy Physics - Theory | |
| dc.title | Discretising differential geometry via a new product on the space of chains | |
| dc.type | text |