Iterated wreath product of the simplex category and iterated loop spaces

Details Iterated wreath product of the simplex category and iterated loop spaces Iterated wreath product of the simplex category and iterated loop spaces

2005-12-26

arxiv.org/abs/math/0512575v2

Adv. Math. 213 (2007) 230-270

Mathematics

Algebraic Topology

Scientific paper

10.1016/j.aim.2006.12.006

Generalising Segal's approach to 1-fold 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 Segal-spectrum associated to a $\Gamma$-space. In particular, each Eilenberg-MacLane space $K(\pi,n)$ has a canonical reduced $\Theta_n$-set model.

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