English

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