Volume 10, issue 4 (2010)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Stems and spectral sequences

Hans Joachim Baues and David Blanc

Algebraic & Geometric Topology 10 (2010) 2061–2078
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.

Keywords
$n$–stem, Postnikov system, spectral sequence, mapping algebra, spiral long exact sequence
Mathematical Subject Classification 2000
Primary: 55T05
Secondary: 18G40, 18G55, 55S45, 55T15, 18G30, 18G10
References
Publication
Received: 1 April 2010
Revised: 10 August 2010
Accepted: 20 August 2010
Published: 8 October 2010
Authors
Hans Joachim Baues
Max-Planck-Institut für Mathematik
Vivatsgasse 7
PO Box 7280
D-53111 Bonn
Germany
David Blanc
Department of Mathematics
University of Haifa
31905 Haifa
Israel