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The Arf-Kervaire Invariant via QX

Part of the Progress in Mathematics book series (PM, volume 273)

Abstract

The objective of this chapter is to study πi(∑X) by identifying it with πi(QX) where QX is the space introduced in Chapter 1 § 1.5.8. Since we are interested in the two-primary part of the stable homotopy groups of spheres we would like to concentrate on the case when X = S0. However, for technical reasons concerned with the mod 2 homology of QX we have to consider the case when X is connected. Fortunately, by virtue of the Kahn-Priddy theorem of Chapter 1 Theorem 1.5.10, it is no restriction to consider only connected X since we can study the case when X = ℝℙ

Keywords

Hopf Algebra Homotopy Class Stable Homotopy Stable Homotopy Group Steenrod Operation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag AG 2009

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