## 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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