Iterated wreath product of the simplex category and iterated loop spaces
Abstract
Generalising Segal's approach to 1fold loop spaces, the homotopy theory of $n$fold loop spaces is shown to be equivalent to the homotopy theory of reduced $\Theta_n$spaces, where $\Theta_n$ is an iterated wreath product of the simplex category $\Delta$. A sequence of functors from $\Theta_n$ to $\Gamma$ allows for an alternative description of the Segalspectrum associated to a $\Gamma$space. In particular, each EilenbergMacLane space $K(\pi,n)$ has a canonical reduced $\Theta_n$set model.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 December 2005
 DOI:
 10.48550/arXiv.math/0512575
 arXiv:
 arXiv:math/0512575
 Bibcode:
 2005math.....12575B
 Keywords:

 Mathematics  Algebraic Topology;
 Mathematics  Category Theory;
 18G30;
 55P48;
 18G55;
 55P20
 EPrint:
 Adv. Math. 213 (2007) 230270