arXiv Analytics

Sign in

arXiv:math/0511645 [math.AT]AbstractReferencesReviewsResources

The space of intervals in a Euclidean space

Shingo Okuyama

Published 2005-11-26Version 1

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.

Comments: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol5/agt-5-62.abs.html
Journal: Algebr. Geom. Topol. 5 (2005) 1555-1572
Categories: math.AT
Subjects: 55P35, 55P40
Related articles: Most relevant | Search more
arXiv:2303.01019 [math.AT] (Published 2023-03-02, updated 2023-09-12)
Vietoris thickenings and complexes are weakly homotopy equivalent
arXiv:1612.02773 [math.AT] (Published 2016-12-08)
Cohomology of Polychromatic Configuration Spaces of Euclidean Space
arXiv:2408.14882 [math.AT] (Published 2024-08-27)
Cellular complexes and embeddings into Euclidean spaces: Möbius strip, torus, and projective plane

Links

Toolbox