Stable and unstable operations in mod p cohomology theories

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

• Publication year

  2006

• Venue

  Algebraic & Geometric Topology

• Publication date

  2006-05-17

• Fields of study

  Mathematics

• Identifiers
  DOI 10.2140/agt.2008.8.1059arXiv math/0605471
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• Algebraic topology

  2020cited by this paper
• The units of a ring spectrum and a logarithmic cohomology operation

  2004cited by this paper
• Localization of André¿Quillen¿Goodwillie towers, and the periodic homology of infinite loopspaces

  2003influential reference
• On the telescopic homotopy theory of spaces

  2000cited by this paper
• The Morava K-theory Hopf Ring for BP

  1996cited by this paper
• Algebraic Topology: New Trends in Localization and Periodicity

  1996cited by this paper
• Stable Operations in Generalized Cohomology

  1995influential reference
• Handbook of algebraic topology

  1995cited by this paper
• Morava K-theories and infinite loop spaces

  1989cited by this paper
• Uniqueness of infinite deloopings for $K$-theoretic spaces.

  1987cited by this paper
• The BP Hopf Invariant

  1986cited by this paper
• The Hopf Ring for Morava K-Theory

  1984cited by this paper
• The Hopf ring for complex cobordism

  1974cited by this paper
• On the formal group laws of unoriented and complex cobordism theory

  1969cited by this paper

• Research Proposal

  2019cites this paper
• ELLIPTIC COHOMOLOGY AND ELLIPTIC CURVES (FELIX KLEIN LECTURES, BONN 2015)

  2016cites this paper
• Isogenies, power operations, and homotopy theory

  2014cites this paper
• Tall-Wraith Monoids

  2011cites this paper
• The Hunting of the Hopf Ring

  2007cites this paper
• Research Proposal 2 Stable and Unstable Cohomology Operations Planned Research 3 the Differential Topology of Loop Spaces 4 Category Theory in Geometry

  year unknowncites this paper