Computing crossed modules induced by an inclusion of a normal subgroup, with applications to homotopy 2-types

Ronald Brown and Christopher D. Wensley

We obtain some explicit calculations of crossed Q-modules induced from a crossed module over a normal subgroup P of Q. By virtue of theorems of Brown and Higgins, this enables the computation of the homotopy 2-types and second homotopy modules of certain homotopy pushouts of maps of classifying spaces of discrete groups.

Keywords: crossed modules, homotopy 2­types, generalized Van Kampen theorem, crossed resolution, Postnikov invariant, classifying spaces of discrete groups.

AMS Classification (1991): 18G10, 20F38, 55P15, 55Q20.

Theory and Applications of Categories, Vol. 2, 1996, No. 1, pp3-16.

TAC Home