Volume form as volume of infinitesimal simplices
Anders Kock
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.
Create a lesson
Related papers
The Kaplansky-Walker Lemma for additive categories
Simion Breaz, Cristian Rafiliu
Actions in varieties of non-associative algebras: a survey
Manuel Mancini
Monoidal structure on Rota-Baxter algebras via augmentation, and free cocycle bialgebras
Li Guo, Yunzhou Xie, Yi Zhang
A characterization of central extensions relative to n-nilpotent objects
Marino Gran, James R. A. Gray
Hanslick's Musical Formalism as a Mathematical Structure - Examining meaning in Music through the Lens of Category Theory
Ilyas Khan
Models for dagger (∞,1)-categories III: Univalent flagged dagger (∞,1)-categories and unitarily complete dagger Segal anima
Keima Akasaka