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Zbl 1061.55013
Sinha, Dev P.
Manifold-theoretic compactifications of configuration spaces. (English)
[J] Sel. Math., New Ser. 10, No. 3, 391-428 (2004). ISSN 1022-1824; ISSN 1420-9020/e

Let $M$ denote a smooth manifold, assumed to lie in some Euclidean space. \par 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.
[Lee P. Neuwirth (Princeton)]

MSC 2000:: *55R80 Discriminantal varieties, configuration spaces
55T99 Spectral sequences

Keywords: configuration space; compactification; stratification; diagonal map; tangent space

Cited in: Zbl 1146.18003

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