Algebraic and Geometric Topology 5 (2005),
paper no. 62, pages 1555-1572.
The space of intervals in a Euclidean space
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.
Configuration space, partial abelian monoid, iterated loop space, space of intervals
AMS subject classification.
Submitted: 15 December 2003.
(Revised: 25 March 2005.)
Accepted: 10 November 2005.
Published: 23 November 2005.
Notes on file formats
Takuma National College of Technology
Kagawa 769-1192, JAPAN
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