Stems and spectral sequences

Baues, Hans Joachim¹ ; Blanc, David²

¹Max-Planck-Institut für Mathematik, Vivatsgasse 7, PO Box 7280, D-53111 Bonn, Germany
²Department of Mathematics, University of Haifa, 31905 Haifa, Israel

Algebraic and Geometric Topology, Tome 10 (2010) no. 4, pp. 2061-2078

Résumé

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.

Détail

DOI : 10.2140/agt.2010.10.2061

Keywords: $n$–stem, Postnikov system, spectral sequence, mapping algebra, spiral long exact sequence

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