Geodesic
The space of intervals in a Euclidean space
Okuyama, Shingo1
1Takuma National College of Technology, Kagawa 769-1192, Japan
Algebraic and Geometric Topology, Tome 5 (2005) no. 4, pp. 1555-1572
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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 ΩnΣnX. In this paper, we introduce a space ℐn(X) of intervals suitably topologized in ℝn with labels in a space X and show that it is weakly homotopy equivalent to ΩnΣnX without the assumption on path-connectivity.

DOI : 10.2140/agt.2005.5.1555
Keywords: configuration space, partial abelian monoid, iterated loop space, space of intervals

Okuyama, Shingo  1

1 Takuma National College of Technology, Kagawa 769-1192, Japan 
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Okuyama, Shingo. The space of intervals in a Euclidean space. Algebraic and Geometric Topology, Tome 5 (2005) no. 4, pp. 1555-1572. doi: 10.2140/agt.2005.5.1555

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