The differentiable chain functor is not homotopy equivalent to the continuous chain functor |
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| Authors: | F. Guillé n |
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| Affiliation: | a Departament d'Àlgebra i Geometria, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain
b Departament de Matemàtica Aplicada I, Universitat Politècnica de Catalunya, Diagonal 647, 08028 Barcelona, Spain |
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| Abstract: | Let S∗ and  be the functors of continuous and differentiable singular chains on the category of differentiable manifolds. We prove that the natural transformation  , which induces homology equivalences over each manifold, is not a natural homotopy equivalence. |
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| Keywords: | Differentiable chains Continuous chains Homology equivalence Homotopy equivalence |
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