Volume form as volume of infinitesimal simplices

Details Volume form as volume of infinitesimal simplices Volume form as volume of infinitesimal simplices

2000-06-02

arxiv.org/abs/math/0006008v1

Mathematics

Category Theory

10 pages

Scientific paper

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.

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