Skip to main content

A whitehead product for track groups

Part of the Lecture Notes in Mathematics book series (LNM,volume 1370)

Abstract

We study a pairing π(ΣmW,X) × π(ΣnW,X) → π(Σm+n−1W,X) which specializes to the classical Whitehead product operation in the case W=S0. If W is a suspension the operation is always trivial, but if W is not a suspension and a product vanishes then a version of the Hopf construction gives rise to an element that can be detected by a generalized Hopf invariant.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   54.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   69.95
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M. Arkowitz; The generalized Whitehead product. Pacific J.M. 12 (1962), 7–23.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. I.M. James; Reduced product spaces. Ann. of Math. 62 (1955), 170–197.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. I.M. James; On spaces with a multiplication. Pacific J.M. 7 (1957), 1083–1100.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. G.W. Whitehead; A generalization of the Hopf invariant. Ann. of Math. 51 (1950), 192–237.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. J.H.C. Whitehead; On adding relations to homotopy groups. Ann. of Math. 42 (1941), 409–429.

    CrossRef  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1989 Springer-Verlag

About this paper

Cite this paper

Hardie, K., Jansen, A. (1989). A whitehead product for track groups. In: Carlsson, G., Cohen, R., Miller, H., Ravenel, D. (eds) Algebraic Topology. Lecture Notes in Mathematics, vol 1370. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0085227

Download citation

  • DOI: https://doi.org/10.1007/BFb0085227

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51118-2

  • Online ISBN: 978-3-540-46160-9

  • eBook Packages: Springer Book Archive