#### Volume 8, issue 2 (2008)

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Stable and unstable operations in mod $p$ cohomology theories

### Andrew Stacey and Sarah Whitehouse

Algebraic & Geometric Topology 8 (2008) 1059–1091
##### Abstract

We consider operations between two multiplicative, complex orientable cohomology theories. Under suitable hypotheses, we construct a map from unstable to stable operations, left-inverse to the usual map from stable to unstable operations. In the main example, where the target theory is one of the Morava K–theories, this provides a simple and explicit description of a splitting arising from the Bousfield–Kuhn functor.

##### Keywords
cohomology operations, Morava K-theories
Primary: 55S25
Secondary: 55P47