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Configuration categories and homotopy automorphisms. (English) Zbl 1436.57036

The author describes how under some geometric conditions on a smooth manifold \(M\) with boundary \(\partial M\) a homotopical model for the pair \((M,\partial M)\) can be obtained from the configuration category of \((M \setminus \partial M)\). The existence of a map from the space of paths in \(w:[0,1] \rightarrow M / \partial M\) with \(w(0) = *\) to \(M \setminus \partial M\) via evaluation at \(1\) gives a simple example of this kind of homotopical model. The configuration category then acts on the homotopical model of \((M, \partial M)\). The arguments are modeled on Segal spaces.

MSC:

57R19 Algebraic topology on manifolds and differential topology
55P65 Homotopy functors in algebraic topology
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References:

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