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The space of intervals in a Euclidean space

Shingo Okuyama

Algebraic & Geometric Topology 5 (2005) 1555–1572

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 n with labels in X is weakly homotopy equivalent to ΩnΣnX. In this paper, we introduce a space n(X) of intervals suitably topologized in n with labels in a space X and show that it is weakly homotopy equivalent to ΩnΣnX without the assumption on path-connectivity.

Keywords
configuration space, partial abelian monoid, iterated loop space, space of intervals
Mathematical Subject Classification 2000
Primary: 55P35
Secondary: 55P40
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Publication
Received: 15 December 2003
Revised: 25 March 2005
Accepted: 10 November 2005
Published: 23 November 2005
Authors
Shingo Okuyama
Takuma National College of Technology
Kagawa 769-1192
Japan