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arXiv · 2204.08969

Couplings and primitives on topological spaces

Jürgen Voigt
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Abstract

For an open covering $\mathcal U$ of a topological space and a mapping $d\colon\mathcal I\to\mathbb{K}$, where $\mathcal I:=\bigl\{(U,V)\in\mathcal U\times\mathcal U;\ U\cap V\ne\varnothing\bigr\}$, we present a context for the existence of a mapping $C\colon\mathcal U\to\mathbb{K}$ satisfying $C_V-C_U=d_{UV}$ for all $(U,V)\in\mathcal I$. The result is applied to a Poincar\'e type theorem concerning distributional potentials. We also put the result into the context of algebraic topology.

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Jürgen Voigt. 2022-04-19. Couplings and primitives on topological spaces. https://arxiv.org/abs/2204.08969

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