David Roberts
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 π k\pi_k for k>2k\gt 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 nn-th homology group of the 2-crossed complex corresponds to the (n+1)(n+1)-homotopy group of the homotopy type it represents, we have to be a little careful with the indexing.

Idea: Use the adjunction 2CrssGrp2Crs \leftrightarrows sGrp and the functorial 2-connected cover in sGrpsGrp to define a functorial 2-connected cover in 2Crs2Crs.

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