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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:
55R80Discriminantal varieties, configuration spaces
55T99Spectral sequences (algebraic topology)