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Manifold-theoretic compactifications of configuration spaces. (English) Zbl 1061.55013

Let \(M\) denote a smooth manifold, assumed to lie in some Euclidean space.
The author presents alternative descriptions of \(C_{n}[M]\), the canonical compactification of the space of configurations of n points in \(M\). These allow the introduction of global coordinates, and using them, the description of a stratification of \(C_{n}[M]\). \(C_{n}[M]\) is shown to be homotopy equivalent to the simplicial compactification. The global coordinates are used to prove projection and diagonal maps satisfy co-simplicial identities.

MSC:

55R80 Discriminantal varieties and configuration spaces in algebraic topology
55T99 Spectral sequences in algebraic topology
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