Infinite sums of Adams operations and cobordism (Q2571061)

The stable operations in \(p\)-local \(K\)-theory can be described in terms of Adams operations as certain infinite sums of Adams operations. The first results in this area are due to \textit{K. Johnson} [Can. Math. Bull. 29, 246--255 (1986; Zbl 0613.55012)]. The aim of the present paper is to study the infinite sums of Adams operations for \(\text{MU}_{(p)}\) and BP. For this, the authors use the results of \textit{F. Clarke}, \textit{M. Crossley} and \textit{S. Whitehouse} [Topology 44, No. 1, 151--174 (2005; Zbl 1065.55011)], thus identifying the ``Adams subalgebra'' of the algebras of operations for these theories. In the final sections the authors show that this subalgebra is precisely the centre of the ring of stable degree zero operations. This identification can be compared to the results of \textit{S. P. Novikov} for MU [Math. USSR, Izv. 1, 827--913 (1967; Zbl 0176.52401)] and of \textit{S. Araki} for BP [Osaka J. Math. 12, 343--356 (1975; Zbl 0328.55012)].