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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The Whitehead products and powers in $W$-topology
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by K. A. Hardie, H. J. Marcum and N. Oda PDF
Proc. Amer. Math. Soc. 131 (2003), 941-951 Request permission

Abstract:

We initiate a study of $W$-topology. This is a modification of ordinary topology in which morphisms exist after smashing with a fixed space $W$. Several classical topics are considered in this setting, inter alia Whitehead products, Hopf invariants and the $E$-$H$-$\Delta$ sequence. The main emphasis is on detection of non-trivial elements in the $W$-homotopy groups of spheres.
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Additional Information
  • K. A. Hardie
  • Affiliation: Department of Mathematics, University of Cape Town, 7700 Rondebosch, South Africa
  • Email: hardieka@iafrica.com
  • H. J. Marcum
  • Affiliation: Department of Mathematics, The Ohio State University at Newark, 1179 University Drive, Newark, Ohio 43055
  • Email: marcum@math.ohio-state.edu
  • N. Oda
  • Affiliation: Department of Applied Mathematics, Faculty of Science, Fukuoka University, Fukuoka 814-0180, Japan
  • Email: odanobu@cis.fukuoka-u.ac.jp
  • Received by editor(s): April 8, 2000
  • Received by editor(s) in revised form: August 30, 2000
  • Published electronically: October 18, 2002
  • Additional Notes: The first author acknowledges support from the Foundation for Research Development and the University of Cape Town via the Topology and Category Theory Group.
  • Communicated by: Ralph Cohen
  • © Copyright 2002 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 131 (2003), 941-951
  • MSC (2000): Primary 55Q15, 55Q20, 55Q25
  • DOI: https://doi.org/10.1090/S0002-9939-02-06833-8
  • MathSciNet review: 1937433