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arXiv · 2608.08811

The $\mathcal{L}$-Calculus for Causal Variational Principles: An Exterior Differential Calculus on Non-Smooth Spaces

Felix Finster·Niky Kamran·Frank van der Top
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Abstract

A differential calculus for causal variational principles is developed, which generalizes the exterior calculus of differential forms and some of the associated differential topological structures to non-smooth spaces. Our calculus includes the exterior derivative, de Rham cohomology, glueing constructions (restrictions and extensions of differential forms, Mayer-Vietoris sequence), a K\"unneth formula and Poincar{\'e}'s lemma. Moreover, we prove versions of Stokes' theorem and the Gau{\ss} divergence theorem. The constructions and results are illustrated by several examples.

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BibTeXRIS

Felix Finster, Niky Kamran, Frank van der Top. 2026-08-09. The $\mathcal{L}$-Calculus for Causal Variational Principles: An Exterior Differential Calculus on Non-Smooth Spaces. https://arxiv.org/abs/2608.08811

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