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Rough geometric integration (2405.16615v1)
Published 26 May 2024 in math.DG and math.FA
Abstract: We introduce a notion of distributional $k$-forms on $d$-dimensional manifolds which can be integrated against suitably regular $k$-submanifolds. Our approach combines ideas from Whitney's geometric integration [Whi57] with those of sewing approaches to rough integration [Gub04, FdLP06].