The plethory of operations in complex topological K-theory
arXiv:2001.01608 · doi:10.2140/akt.2021.6.481
Abstract
We provide a concrete introduction to the topologised, graded analogue of an algebraic structure known as a plethory, originally due to Tall and Wraith. Stacey and Whitehouse showed this structure is present on the cohomology operations for a suitable generalised cohomology theory. We compute an explicit expression for the plethory of operations for complex topological K-theory. This is formulated in terms of a plethory enhanced with structure corresponding to the looping of operations. In this context we show that the familiar lambda operations generate all the operations.
17 pages, minor changes, to appear in Annals of K-theory