Stable and unstable operations in mod p cohomology theories

Stacey, Andrew; Whitehouse, Sarah

doi:10.2140/agt.2008.8.1059

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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 2000

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/

Volume 8, issue 2 (2008)