# name
The differentiable chain functor is not homotopy equivalent to the continuous chain functor

# metadata.dc.description.abstract[].value
Let $S_*$ and $S_*^\{infty}$ be the functors of continuous and differentiable singular chains on the category of differentiable manifolds. We prove that the natural transformation $i: S_*^\infty \rightarrow S_*$, which induces homology equivalences over each manifold, is not a natural homotopy equivalence.

# metadata.dc.relation.ispartof[].value
Topology and its Applications, 2009, vol. 156, num. 3, p. 658-660

# metadata.dc.source[].value
Articles publicats en revistes (Matemàtiques i Informàtica)

# metadata.dc.title[].value
The differentiable chain functor is not homotopy equivalent to the continuous chain functor