Iterated wreath product of the simplex category and iterated loop spaces
Abstract
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.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- December 2005
- DOI:
- 10.48550/arXiv.math/0512575
- arXiv:
- arXiv:math/0512575
- Bibcode:
- 2005math.....12575B
- Keywords:
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- Mathematics - Algebraic Topology;
- Mathematics - Category Theory;
- 18G30;
- 55P48;
- 18G55;
- 55P20
- E-Print:
- Adv. Math. 213 (2007) 230-270