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arXiv · 2408.04263

Poincar\'e's lemma for formal manifolds

Fulin Chen·Binyong Sun·Chuyun Wang
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Abstract

This is a paper in a series that studies smooth relative Lie algebra homologies and cohomologies based on the theory of formal manifolds and formal Lie groups. In two previous papers, we develop the basic theory of formal manifolds, including generalizations of vector-valued distributions and generalized functions on smooth manifolds to the setting of formal manifolds. In this paper, we establish Poincar\'e's lemma for de Rham complexes with coefficients in formal functions, formal generalized functions, compactly supported formal densities, or compactly supported formal distributions.

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Fulin Chen, Binyong Sun, Chuyun Wang. 2024-08-08. Poincar\'e's lemma for formal manifolds. https://arxiv.org/abs/2408.04263

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