2-connected cover of a 2-crossed complex

A 2-crossed complex is an algebraic model of a homotopy type such that the homotopy groups ${\pi}_{k}$ for $k>2$ have trivial Whitehead products.

As such, the 2-connected cover should be modeled by a (bounded) chain complex. The aim is to define a functorial 2-connected cover of a 2-crossed complex.

Note that since the $n$-th homology group of the 2-crossed complex corresponds to the $(n+1)$-homotopy group of the homotopy type it represents, we have to be a little careful with the indexing.

**Idea:** Use the adjunction $2\mathrm{Crs}\leftrightarrows \mathrm{sGrp}$ and the functorial 2-connected cover in $\mathrm{sGrp}$ to define a functorial 2-connected cover in $2\mathrm{Crs}$.

Created on July 27, 2010 06:11:09
by David Roberts
(203.24.207.80)