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

Sinha, Dev P.

Sel. Math., New Ser. 10, No. 3, 391-428 (2004).

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.

Reviewer: Lee P. Neuwirth (Princeton)

MSC:

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

Keywords:

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