Mathematics Preprints 1995
95.03 : R. Brown & C.D. Wensley
On finite induced crossed modules, and the homotopy 2-type of mapping cones
Abstract:Results on the finiteness of induced crossed modules are proved both algebraically and topologically. Using the Van Kampen type theorem for the fundamental crossed module, applications are given to the 2-types of mapping cones of classifying spaces of groups. Calculations of the cohomology classes of some finite crossed modules are given, using crossed complex methods.
Published in:Theory and Applications of Categories, 1(3) (1995) 54-71.
95.04 : R. Brown & C.D. Wensley
Computing crossed modules induced by an inclusion of a normal subgroup, with applications to homotopy 2-types
Abstract: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.
Published in:Theory and Applications of Categories, 2(1) (1996) 3-16.
95.08 : R. Brown, M. Golasinski, T. Porter, & A. Tonks
Spaces of maps into classifying spaces for equivariant crossed complexes
Abstract:We give an equivariant version of the homotopy theory of crossed complexes. The applications generalise work on equivariant Ellenberg-MacLane spaces, including the non-abelian case of dimension 1, and on local systems. It also generalises the theory of equivariant 2-types, due to Moerdyk and Svensson. Further we give results not just on the homotopy classification of maps but also on the homotopy types of certain equivariant function spaces.
AMS Subject Classification:55P91, 55U10, 55U35