English

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