English

The Hunting of the Hopf Ring

Algebraic Topology 2007-11-26 v1 K-Theory and Homology Rings and Algebras

Abstract

We provide a new algebraic description of the structure on the set of all unstable cohomology operations for a suitable generalised cohomology theory, E^*. Our description is as a graded and completed version of a Tall-Wraith monoid. The E^*-cohomology of a space X is a module for this Tall-Wraith monoid. We also show that the corresponding Hopf ring of unstable co-operations is a module for the Tall-Wraith monoid of unstable operations. Further examples are provided by considering operations from one theory to another.

Keywords

Cite

@article{arxiv.0711.3722,
  title  = {The Hunting of the Hopf Ring},
  author = {Andrew Stacey and Sarah Whitehouse},
  journal= {arXiv preprint arXiv:0711.3722},
  year   = {2007}
}

Comments

61 pages, no figures; uses xy, pxfonts