The plethory of operations in complex topological K-theory
K-Theory and Homology
2021-09-15 v2
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.
Keywords
Cite
@article{arxiv.2001.01608,
title = {The plethory of operations in complex topological K-theory},
author = {William Mycroft and Sarah Whitehouse},
journal= {arXiv preprint arXiv:2001.01608},
year = {2021}
}
Comments
17 pages, minor changes, to appear in Annals of K-theory