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arXiv:1208.2184 [math.AT]AbstractReferencesReviewsResources

The realizability of operations on homotopy groups concentrated in two degrees

Hans-Joachim Baues, Martin Frankland

Published 2012-08-10, updated 2014-07-09Version 2

The homotopy groups of a space are endowed with homotopy operations which define the \Pi-algebra of the space. An Eilenberg-MacLane space is the realization of a \Pi-algebra concentrated in one degree. In this paper, we provide necessary and sufficient conditions for the realizability of a \Pi-algebra concentrated in two degrees. We then specialize to the stable case, and list infinite families of such \Pi-algebras that are not realizable.

Comments: Version 2: Some minor corrections. A few changes to the exposition. To appear in the Journal of Homotopy and Related Structures
Categories: math.AT
Subjects: 55Q35, 55Q40, 55Q45, 55Q15, 55P20
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