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Proceedings of the American Mathematical Society

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Some remarks on configuration spaces

Author: George Raptis
Journal: Proc. Amer. Math. Soc. 139 (2011), 1879-1887
MSC (2010): Primary 55R80; Secondary 57N99
Published electronically: October 6, 2010
MathSciNet review: 2763775
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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.

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George Raptis
Affiliation: Institut für Mathematik, Universität Osnabrück, Albrechtstrasse 28a, 49069 Osnabrück, Germany

Keywords: Configuration spaces, cell-like maps
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
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.