## Some remarks on configuration spaces

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- by George Raptis PDF
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**139**(2011), 1879-1887 Request permission

## Abstract:

This paper studies the homotopy type of the configuration spaces $F_n(X)$ by introducing the idea of configuration spaces of maps. For every map $f: X \to Y$, the configuration space $F_n(f)$ is the space of configurations in $X$ that have distinct images in $Y$. We show that the natural maps $F_n(X) \leftarrow F_n(f) \rightarrow F_n(Y)$ are homotopy equivalences when $f$ is a proper cell-like map between $d$-manifolds. We also show that the best approximation to $X \mapsto F_n(X)$ by a homotopy invariant functor is given by the $n$-fold product map.## References

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## Additional Information

**George Raptis**- Affiliation: Institut für Mathematik, Universität Osnabrück, Albrechtstrasse 28a, 49069 Osnabrück, Germany
- Email: graptis@mathematik.uni-osnabrueck.de
- Received by editor(s): April 30, 2010
- Received by editor(s) in revised form: May 11, 2010
- Published electronically: October 6, 2010
- Communicated by: Brooke Shipley
- © Copyright 2010
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc.
**139**(2011), 1879-1887 - MSC (2010): Primary 55R80; Secondary 57N99
- DOI: https://doi.org/10.1090/S0002-9939-2010-10580-4
- MathSciNet review: 2763775