Group Operads and Homotopy Theory

Details Group Operads and Homotopy Theory Group Operads and Homotopy Theory

2011-11-30

arxiv.org/abs/1111.7090v1

Mathematics

Algebraic Topology

38 pages, part of the author's Ph.D. thesis

Scientific paper

We give an algebraic characterization of topological $K(\pi,1)$ operads by and reconstruct them from their fundamental groups operads. This characterization can be used to produce algebraic models for some canonical objects in homotopy theory. For instance, we obtain a free group model for the canonical stabilization $\Omega^2 \Sigma^2 X \hookrightarrow \Omega^{\infty} \Sigma^{\infty} X$, in particular a free group model for its homotopy fibre.

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