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arXiv 0804.20002008-04-12math.KT

Homotopy types of reduced 2-nilpotent simplicial groups

Hans-Joachim Baues, Roman Mikhailov

发表信息：: Ind. J. Pure Appl. Math. 40 (2009), 35-80

英文摘要：

We classify the homotopy types of reduced 2-nilpotent simplicial groups in terms of the homology an d boundary invariants $b,β$. This contains as special cases results of J.H.C. Whitehead on 1-connected 4-dimensional complexes and of Quillen on reduced 2-nilpotent rational simplicial groups. Moreover it yields for 1-nilpotent (or abelian) simplicial groups a classification due to Dold-Kan. Our result describes a new natural structure of the integral homology of any simply connected space. We also classify the homotopy types of connective spectra in the category of 2-nilpotent simplicial groups. Moreover we compute homotopy groups of spheres in the category of $m$-nilpotent groups for $m=2,3$ and partially for $m=4,5$.

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