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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The Whitehead products and powers in $W$-topology


Authors: K. A. Hardie, H. J. Marcum and N. Oda
Journal: Proc. Amer. Math. Soc. 131 (2003), 941-951
MSC (2000): Primary 55Q15, 55Q20, 55Q25
Published electronically: October 18, 2002
MathSciNet review: 1937433
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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

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06833-8
PII: S 0002-9939(02)06833-8
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
Article copyright: © Copyright 2002 American Mathematical Society