The Hunting of the Hopf Ring

Andrew Stacey; Sarah Whitehouse

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arXiv · 0711.3722

The Hunting of the Hopf Ring

Andrew Stacey·Sarah Whitehouse

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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.

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Andrew Stacey, Sarah Whitehouse. 2007-11-23. The Hunting of the Hopf Ring. https://arxiv.org/abs/0711.3722

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