The space of intervals in a Euclidean space
Algebraic Topology
2014-10-01 v1
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 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.
Keywords
Cite
@article{arxiv.math/0511645,
title = {The space of intervals in a Euclidean space},
author = {Shingo Okuyama},
journal= {arXiv preprint arXiv:math/0511645},
year = {2014}
}
Comments
Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol5/agt-5-62.abs.html