Volume form as volume of infinitesimal simplices
Category Theory
2007-05-23 v1 Differential Geometry
Abstract
In the context of Synthetic Differential Geometry, we describe the square volume of a ``second-infinitesimal simplex'', in terms of square-distance between its vertices. The square-volume function thus described is symmetric in the vertices. The square-volume gives rise to a characterization of the volume form in the top dimension.
Keywords
Cite
@article{arxiv.math/0006008,
title = {Volume form as volume of infinitesimal simplices},
author = {Anders Kock},
journal= {arXiv preprint arXiv:math/0006008},
year = {2007}
}
Comments
10 pages