The Hunting of the Hopf Ring

Details The Hunting of the Hopf Ring The Hunting of the Hopf Ring

2007-11-23

arxiv.org/abs/0711.3722v1

Mathematics

Algebraic Topology

61 pages, no figures; uses xy, pxfonts

Scientific paper

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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