invertible spectra smashing with the SmithToda spectrum at the prime
Authors:
Ippei Ichigi and Katsumi Shimomura
Journal:
Proc. Amer. Math. Soc. 132 (2004), 31113119
MSC (2000):
Primary 55Q99; Secondary 55Q45, 55Q51
Published electronically:
June 2, 2004
MathSciNet review:
2063134
Fulltext PDF Free Access
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Abstract: Let denote the Bousfield localization functor with respect to the JohnsonWilson spectrum . A spectrum is called invertible if there is a spectrum such that . Hovey and Sadofsky, Invertible spectra in the local stable homotopy category, showed that every invertible spectrum is homotopy equivalent to a suspension of the local sphere at a prime . At the prime , it is shown, A relation between the Picard group of the local homotopy category and based Adams spectral sequence, that there exists an invertible spectrum that is not homotopy equivalent to a suspension of . In this paper, we show the homotopy equivalence for the SmithToda spectrum . In the same manner as this, we also show the existence of the selfmap that induces on the homology.
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Additional Information
Ippei Ichigi
Affiliation:
Department of Mathematics, Faculty of Science, Kochi University, Kochi, 7808520, Japan
Email:
95sm004@math.kochiu.ac.jp
Katsumi Shimomura
Affiliation:
Department of Mathematics, Faculty of Science, Kochi University, Kochi, 7808520, Japan
Email:
katsumi@math.kochiu.ac.jp
DOI:
http://dx.doi.org/10.1090/S0002993904073873
PII:
S 00029939(04)073873
Keywords:
Invertible spectrum,
SmithToda spectrum,
homotopy groups
Received by editor(s):
November 20, 2002
Received by editor(s) in revised form:
May 23, 2003
Published electronically:
June 2, 2004
Communicated by:
Paul Goerss
Article copyright:
© Copyright 2004
American Mathematical Society
