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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Some remarks on configuration spaces
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by George Raptis PDF
Proc. Amer. Math. Soc. 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.
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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