Stems and Spectral Sequences
Algebraic Topology
2014-10-01 v1
Abstract
We introduce the category Pstem[n] of n-stems, with a functor P[n] from spaces to Pstem[n]. This can be thought of as the n-th order homotopy groups of a space. We show how to associate to each simplicial n-stem Q an (n+1)-truncated spectral sequence. Moreover, if Q=P[n]X is the Postnikov n-stem of a simplicial space X, the truncated spectral sequence for Q is the truncation of the usual homotopy spectral sequence of X. Similar results are also proven for cosimplicial n-stems. They are helpful for computations, since n-stems in low degrees have good algebraic models.
Cite
@article{arxiv.1008.4266,
title = {Stems and Spectral Sequences},
author = {Hans-Joachim Baues and David Blanc},
journal= {arXiv preprint arXiv:1008.4266},
year = {2014}
}