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5 - The σ-Orientation

Published online by Cambridge University Press:  23 November 2018

Eric Peterson
Affiliation:
Harvard University, Massachusetts
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Summary

In this chapter, we bring the results of the preceding four chapters to bear on the problem of understanding String bordism, first using its lower–connectivity analogues and its complex analogue to paint a landscape into which these results naturally fit. Our overall strategy is again guided by the structure of the moduli of formal groups, which leads us to pursue a calculation of the Morava E–theory of complex bordism spectra before bringing us to the general topological results we seek. We conclude with a summary of unpublished results of Ando, Hopkins, and Strickland on the String–orientation of elliptic field spectra. We also include an extended discussion of elliptic curves, specialized to the context most relevant to us, for the reader’s convenience.

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Publisher: Cambridge University Press
Print publication year: 2018

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  • The σ-Orientation
  • Eric Peterson, Harvard University, Massachusetts
  • Book: Formal Geometry and Bordism Operations
  • Online publication: 23 November 2018
  • Chapter DOI: https://doi.org/10.1017/9781108552165.008
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  • The σ-Orientation
  • Eric Peterson, Harvard University, Massachusetts
  • Book: Formal Geometry and Bordism Operations
  • Online publication: 23 November 2018
  • Chapter DOI: https://doi.org/10.1017/9781108552165.008
Available formats
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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.

  • The σ-Orientation
  • Eric Peterson, Harvard University, Massachusetts
  • Book: Formal Geometry and Bordism Operations
  • Online publication: 23 November 2018
  • Chapter DOI: https://doi.org/10.1017/9781108552165.008
Available formats
×