The space of intervals in a Euclidean space

Details The space of intervals in a Euclidean space The space of intervals in a Euclidean space

2005-11-26

arxiv.org/abs/math/0511645v1

Algebr. Geom. Topol. 5 (2005) 1555-1572

Mathematics

Algebraic Topology

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol5/agt-5-62.abs.html

Scientific paper

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

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