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2009-01-01

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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/34541

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

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http://dx.doi.org/10.1016/j.topol.2008.09.005

Abstract

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.

Subject

Topologia diferencial, Topologia algebraica, Àlgebra homològica

Subject (English)

Differential topology, Algebraic topology, Homological algebra

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Articles publicats en revistes (Matemàtiques i Informàtica)

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GUILLÉN SANTOS, Francisco, et al. The differentiable chain functor is not homotopy equivalent to the continuous chain functor. Topology and its Applications. 2009. Vol. 156, num. 3, pags. 658-660. ISSN 0166-8641. [consulted: 12 of June of 2026]. Available at: https://hdl.handle.net/2445/34541

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