We introduce the category of –stems, with a functor from spaces to . This can be thought of as the –th order homotopy groups of a space. We show how to associate to each simplicial –stem an –truncated spectral sequence. Moreover, if is the Postnikov –stem of a simplicial space , the truncated spectral sequence for is the truncation of the usual homotopy spectral sequence of . Similar results are also proven for cosimplicial –stems. They are helpful for computations, since –stems in low degrees have good algebraic models.
"Stems and spectral sequences." Algebr. Geom. Topol. 10 (4) 2061 - 2078, 2010. https://doi.org/10.2140/agt.2010.10.2061