Joint with Sarah Whitehouse

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.

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• On the arXiv as math.AT/0605471
• Published version in Algebraic & Geometric Topology 8 (2008) 1059-1091 (DOI: 10.2140/agt.2008.8.1059)