Algebraic & Geometric Topology 5 (2005) 1555–1572

DOI: 10.2140/agt.2005.5.1555

arXiv: math.AT/0511645

Abstract

For a path-connected space X, a well-known theorem of Segal, May and Milgram asserts that the configuration space of finite points in Rⁿ with labels in X is weakly homotopy equivalent to ΩⁿΣⁿ X. In this paper, we introduce a space I_n(X) of intervals suitably topologized in Rⁿ with labels in a space X and show that it is weakly homotopy equivalent to ΩⁿΣⁿ X without the assumption on path-connectivity.

Keywords

configuration space, partial abelian monoid, iterated loop space, space of intervals

Mathematical Subject Classification

Primary: 55P35

Secondary: 55P40

References

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Publication

Received: 15 December 2003
Revised: 25 March 2005
Accepted: 10 November 2005
Published: 23 November 2005

Authors