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Demonstrates the injectivity of relative Gelfand–Fuks cohomology in spheres, correcting previous claims.
We study the Gelfand–Fuks cohomology of smooth vector fields on relative to following a method of Haefliger that uses tools from rational homotopy theory. In particular, we show that injects into the relative Gelfand–Fuks cohomology which corrects a claim by Haefliger. Moreover, for the relative Gelfand–Fuks cohomology agrees with the smooth cohomology of and we provide a computation in low degrees.
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Nils Prigge (2026) studied this question.
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