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On the homology of configuration spaces. (English) Zbl 0689.55012
The authors determine the additive structure of the homology of certain configuration spaces. In particlar, let $$C^ k(M)$$ or $$F(M,k)/\Sigma_ k$$ denote the configuration space of unordered k-tuples of distinct points in a space M. If M. is a smooth compact manifold, the authors determine the homology of $$C^ k(M)$$ in the following cases: (1) coefficients are taken in any field and M is odd dimensional and (2) coefficients are taken in $${\mathbb{Z}}/2{\mathbb{Z}}$$ and M is even dimensional. These results agree with previous results obtained by the reviewer when M is Euclidean space. The mod 2 results overlap with some recent results of P. Löffler and J. Milgram. Some analogous results for even dimensional manifolds will appear in work of C.-F. Bödigheimer, the reviewer, and J. Milgram.
Reviewer: F.Cohen

##### MSC:
 55P99 Homotopy theory
##### Keywords:
smooth compact manifold
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