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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The homotopy groups of the $L_2$-localized Toda-Smith spectrum $V(1)$ at the prime 3


Author: Katsumi Shimomura
Journal: Trans. Amer. Math. Soc. 349 (1997), 1821-1850
MSC (1991): Primary 55Q45, 55Q10, 55Q52
MathSciNet review: 1370651
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Abstract: In this paper, we try to compute the homotopy groups of the $L_2$-localized Toda-Smith spectrum $V(1)$ at the prime 3 by using the Adams-Novikov spectral sequence, and have almost done so. This computation involves non-trivial differentials $d_5$ and $d_9$ of the Adams-Novikov spectral sequence, different from the case $p>3$. We also determine the homotopy groups of some $L_2$-localized finite spectra relating to $V(1)$. We further show some of the non-trivial differentials on elements relating so-called $\beta $-elements in the Adams-Novikov spectral sequence for $\pi _*(S^0)$.


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Additional Information

Katsumi Shimomura
Affiliation: Faculty of Education, Tottori University, Tottori, 680, Japan
Email: katsumi@fed.tottori-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9947-97-01710-8
PII: S 0002-9947(97)01710-8
Received by editor(s): October 31, 1995
Article copyright: © Copyright 1997 American Mathematical Society