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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

DOI: 10.2140/agt.2008.8.1059
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
Mathematical Subject Classification

Primary: 55S25

Secondary: 55P47
References
Publication

Received: 17 October 2006
Revised: 16 May 2008
Accepted: 19 May 2008
Published: 6 July 2008
Authors
Andrew Stacey
Institutt for Matematiske fag
NTNU
7491 Trondheim
Norway
http://www.math.ntnu.no/~stacey
Sarah Whitehouse
Department of Pure Mathematics
University of Sheffield
Sheffield S3 7RH
United Kingdom
http://www.sarah-whitehouse.staff.shef.ac.uk/