Note on beta elements in homotopy, and an application to the prime three case
Author:
Katsumi Shimomura
Journal:
Proc. Amer. Math. Soc. 138 (2010), 14951499
MSC (2010):
Primary 55Q45
Published electronically:
December 8, 2009
MathSciNet review:
2578544
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Abstract: Let denote the sphere spectrum localized at an odd prime . Then we have the first beta element , whose cofiber we denote by . We also consider a generalized SmithToda spectrum characterized by . In this note, we show that an element of gives rise to a beta element of homotopy groups of spheres. As an application, we show the existence of at the prime three to complete a conjecture of Ravenel's: exists if and only if is not congruent to , or mod .
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Additional Information
Katsumi Shimomura
Affiliation:
Department of Mathematics, Faculty of Science, Kochi University, Kochi, 7808520, Japan
Email:
katsumi@kochiu.ac.jp
DOI:
http://dx.doi.org/10.1090/S0002993909101909
Received by editor(s):
April 19, 2009
Published electronically:
December 8, 2009
Communicated by:
Brooke Shipley
Article copyright:
© Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
