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A quick proof of the rational Hurewicz theorem and a computation of the rational homotopy groups of spheres

Published online by Cambridge University Press:  21 April 2004

STEPHAN KLAUS  and
MATTHIAS KRECK
STEPHAN KLAUS
Affiliation:
Mathematisches Forschungsinstitut, Oberwolfach, Lorenzenhof, 77709 Oberwolfach-Walke, Germany. e-mail: [email protected]
MATTHIAS KRECK
Affiliation:
Mathematisches Institut, Universität Heidelberg, Im Neuenheimer Feld 188, 69120 Heidelberg, Germany. e-mail: [email protected]
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Abstract

We give an elementary proof of the rational Hurewicz theorem and compute the rational cohomology groups of Eilenberg–MacLane spaces and the rational homotopy groups of spheres. Instead of using the Serre spectral sequence, we only assume the classical Hurewicz theorem, and give a short proof of the rational Gysin and Wang long exact sequences, which are applied inductively to the path fibration of Eilenberg–MacLane spaces.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 136 , Issue 3 , May 2004 , pp. 617 - 623
Copyright
2004 Cambridge Philosophical Society

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