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- W2327728909 abstract "Shadow forms. Consider a simplicial complex K. Whitney associated to each simplicial cochain 4 a differential form v(4) on K. Whitney's map v from simplicial cochains to differential forms is a map of cochain complexes which induces the deRham isomorphism. We call the forms v(4) Whitney forms. They have been useful in several contexts, most notably integral geometry and rational homotopy theory. In this paper, we introduce a generalization of Whitney forms called shadow forms. We associate to certain simplicial chains g with respect to the first derived subdivision K' of K a shadow form w(() on K. Let us illustrate the construction of shadow forms when K is a single n-simplex, which we now denote by A. In this case, w(g) is defined for k-simplices g of AX' which do not lie in the boundary of (or for linear combinations of these). For example, if A is the 2-simplex, then either of the 1-simplices (, or (2 pictured below has an associated shadow form." @default.
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- W2327728909 date "1991-12-01" @default.
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- W2327728909 title "Simplicial Differential Forms with Poles" @default.
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- W2327728909 doi "https://doi.org/10.2307/2374899" @default.
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