Operations which detect 𝒫¹ in odd primary connective K-theory

Kohhei Yamaguchi

Vol. 130 (1987), No. 1, 195–208

DOI: 10.2140/pjm.1987.130.195

Abstract

Let G denote the Adams summand of connective unitary K-theory spectrum at the odd prime integer p. In this paper, we study maps ϕ : G → G which have two properties

1. ϕ_∗ = 0 : π₀(G) → π₀(G),
2. ϕ_∗(v) = p𝜖v with the unit 𝜖 ∈ Z_(p)^×,

where π_∗(G) = Z_(p)[v] and |v| = 2(p − 1). An example of such operations is the Adams operation ψ^p+1 − 1, and we will give an elementary proof of non-existence of elements of mod p Hopf invariant one.

Mathematical Subject Classification 2000

Primary: 55S25

Secondary: 55N20, 55P42, 55Q25

Milestones

Received: 24 April 1986

Published: 1 November 1987