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Hurewicz Images, BP-theory and the Arf-Kervaire Invariant

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

Abstract

The objective of this chapter is to prove the conjecture of [30] in its original form, as stated in Chapter 1, Theorem 1.8.10. This result is reiterated in this chapter as Theorem 7.2.2. The conjecture states that an element of \( \pi _{2^{n + 1} - 2} (\sum ^\infty \mathbb{R}\mathbb{P}^\infty ) \) corresponds under the Kahn-Priddy map to the class of a framed manifold of Arf-Kervaire invariant one if and only if it has a non-zero Hurewicz image in ju-theory. I shall prove this result in three ways (§§7.2.3-7.2.5)-one of which uses an excursion into BP-theory.

Keywords

Mapping Cone Homology Theory Stable Homotopy Group Cohomology Operation Thom Class 
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Copyright information

© Birkhäuser Verlag AG 2009

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