The differentiable chain functor is not homotopy equivalent to the continuous chain functor
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 equiv...
| Autores: | , , , |
|---|---|
| Tipo de documento: | artigo |
| Estado: | Versión aceptada para publicación |
| Data de publicação: | 2009 |
| País: | España |
| Recursos: | Universidad de Barcelona |
| Repositório: | Dipòsit Digital de la UB |
| OAI Identifier: | oai:diposit.ub.edu:2445/34541 |
| Acesso em linha: | https://hdl.handle.net/2445/34541 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Topologia diferencial Topologia algebraica Àlgebra homològica Differential topology Algebraic topology Homological algebra |
| Resumo: | 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. |
|---|