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2010 Stems and spectral sequences
Hans Joachim Baues, David Blanc
Algebr. Geom. Topol. 10(4): 2061-2078 (2010). DOI: 10.2140/agt.2010.10.2061

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.

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Hans Joachim Baues. David Blanc. "Stems and spectral sequences." Algebr. Geom. Topol. 10 (4) 2061 - 2078, 2010. https://doi.org/10.2140/agt.2010.10.2061

Information

Received: 1 April 2010; Revised: 10 August 2010; Accepted: 20 August 2010; Published: 2010
First available in Project Euclid: 19 December 2017

zbMATH: 1202.55010
MathSciNet: MR2728484
Digital Object Identifier: 10.2140/agt.2010.10.2061

Subjects:
Primary: 55T05
Secondary: 18G10, 18G30, 18G40, 18G55, 55S45, 55T15

Rights: Copyright © 2010 Mathematical Sciences Publishers

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