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4 - Unstable Cooperations

Published online by Cambridge University Press:  23 November 2018

Eric Peterson
Affiliation:
Harvard University, Massachusetts
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Summary

This chapter approaches aspects of unstable homotopy theory from the perspective of the preceding chapter: We study the unstable analog of effective descent and thereby embark on an analysis of the algebro–geometric objects that arise from these considerations. This lends a modern perspective on a variety of classical topics: Hopf rings, the Ravenel–Wilson results on the infinite loopspaces associated to BP, Dieudonné theory, Brown–Gitler spectra, and the formal schemes associated to Eilenberg–Mac Lane spaces. We also include a novel discussion of the functorial algebraic geometry of Hopf rings, which gives a reinterpretation of the central Ravenel–Wilson relation and exerts an overall influence on our presentation of the other materials.

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Publisher: Cambridge University Press
Print publication year: 2018

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  • Unstable Cooperations
  • Eric Peterson, Harvard University, Massachusetts
  • Book: Formal Geometry and Bordism Operations
  • Online publication: 23 November 2018
  • Chapter DOI: https://doi.org/10.1017/9781108552165.007
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  • Unstable Cooperations
  • Eric Peterson, Harvard University, Massachusetts
  • Book: Formal Geometry and Bordism Operations
  • Online publication: 23 November 2018
  • Chapter DOI: https://doi.org/10.1017/9781108552165.007
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Unstable Cooperations
  • Eric Peterson, Harvard University, Massachusetts
  • Book: Formal Geometry and Bordism Operations
  • Online publication: 23 November 2018
  • Chapter DOI: https://doi.org/10.1017/9781108552165.007
Available formats
×