Homotopy types of reduced 2-nilpotent simplicial groups
K-Theory and Homology
2010-09-01 v1
Abstract
We classify the homotopy types of reduced 2-nilpotent simplicial groups in terms of the homology an d boundary invariants . 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 -nilpotent groups for and partially for .
Cite
@article{arxiv.0804.2000,
title = {Homotopy types of reduced 2-nilpotent simplicial groups},
author = {Hans-Joachim Baues and Roman Mikhailov},
journal= {arXiv preprint arXiv:0804.2000},
year = {2010}
}