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Volume form as volume of infinitesimal simplices

Anders Kock
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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.

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Anders Kock. 2000-06-02. Volume form as volume of infinitesimal simplices. https://arxiv.org/abs/math/0006008

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