Stable Homotopy Around the Arf-Kervaire Invariant pp 119-142 | Cite as

# Real Projective Space

Chapter

## Abstract

The objective of this chapter is to present the cohomological calculations (in and related Whitehead product maps. In [30] it is shown that if

*MU**,*KU** and -BP*) which will be needed in this and later chapters for the study of maps of the form$$
g:\sum ^\infty S^{2^{k + 1} - 2} \to \sum ^\infty \mathbb{R}\mathbb{P}^{2^{k + 1} - 2}
$$

*g** is non-zero on*jo**-theory, which was introduced in Chapter 1, Example 1.3.4(iv), then*g*is detected by*Sq*^{ 2k }. On the other hand detection by*jo**-theory is equivalent to the*KU**-e-invariant (defined by means of ψ^{3}-1) being \( \frac{{(3^{2^k } - 1)(2w + 1)}} {4} \). The calculations of this chapter will eventually be used to prove both this and the converse result (conjectured in [30]) in Chapter 8, Theorem 8.1.2.## Keywords

Real Projective Space Whitehead Product Thom Class Adams Operation Homotopy Commutative Diagram
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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