The realizability of operations on homotopy groups concentrated in two degrees
arXiv:1208.2184 · doi:10.1007/s40062-014-0086-3
Abstract
The homotopy groups of a space are endowed with homotopy operations which define the Π-algebra of the space. An Eilenberg-MacLane space is the realization of a Π-algebra concentrated in one degree. In this paper, we provide necessary and sufficient conditions for the realizability of a Π-algebra concentrated in two degrees. We then specialize to the stable case, and list infinite families of such Π-algebras that are not realizable.
Version 2: Some minor corrections. A few changes to the exposition. To appear in the Journal of Homotopy and Related Structures