NOTE ON THE WHITEHEAD PRODUCT

Abstract

This chapter discusses the Whitehead product, [α, β] ε π p+q–1 (Sn), where α ε πp (Sn), β ε πp (Sn), and [α, β] is the product α·β. It also presents the proof of Pι4 = 2γ – E Jμ, where γε π7 (S4) is the Hopf element and μ is a generator of π3 (R3). Thus, Jμ is a Blakers–Massey element of π6 (S3), with HJμ = α5. The chapter also presents an assumption where S2 is referred to a quaterionic coordinate, q, with unit norm, in such a way that αn corresponds to the unity, q=1. Then, S2 corresponds to the imaginary quaternions.