Algebraic and Geometric Topology 5 (2005), paper no. 62, pages 1555-1572.

The space of intervals in a Euclidean space

Shingo Okuyama


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. Configuration space, partial abelian monoid, iterated loop space, space of intervals

AMS subject classification. Primary: 55P35. Secondary: 55P40.

E-print: arXiv:math.AT/0511645

DOI: 10.2140/agt.2005.5.1555

Submitted: 15 December 2003. (Revised: 25 March 2005.) Accepted: 10 November 2005. Published: 23 November 2005.

Notes on file formats

Shingo Okuyama
Takuma National College of Technology
Kagawa 769-1192, JAPAN
Email: okuyama@dc.takuma-ct.ac.jp

AGT home page

EMIS/ELibM Electronic Journals

Outdated Archival Version

These pages are not updated anymore. They reflect the state of 21 Apr 2006. For the current production of this journal, please refer to http://msp.warwick.ac.uk/.