Algebraic & Geometric Topology

Stable and unstable operations in mod $p$ cohomology theories

Andrew Stacey and Sarah Whitehouse

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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.

Article information

Source
Algebr. Geom. Topol., Volume 8, Number 2 (2008), 1059-1091.

Dates
Received: 17 October 2006
Revised: 16 May 2008
Accepted: 19 May 2008
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513796856

Digital Object Identifier
doi:10.2140/agt.2008.8.1059

Mathematical Reviews number (MathSciNet)
MR2443108

Zentralblatt MATH identifier
1153.55016

Subjects
Primary: 55S25: $K$-theory operations and generalized cohomology operations [See also 19D55, 19Lxx]
Secondary: 55P47: Infinite loop spaces

Keywords
cohomology operations Morava K-theories

Citation

Stacey, Andrew; Whitehouse, Sarah. Stable and unstable operations in mod $p$ cohomology theories. Algebr. Geom. Topol. 8 (2008), no. 2, 1059--1091. doi:10.2140/agt.2008.8.1059. https://projecteuclid.org/euclid.agt/1513796856


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