Journal of the Mathematical Society of Japan

The homotopy groups of the L2-localized mod 3 Moore spectrum

Katsumi SHIMOMURA

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Abstract

At each prime number p, the homotopy groups π*(L2S0) of the v2-1BP-localized sphere spectrum play an crucial role to understand the category of v2-1BP-local spectra. For p>3, they are determined by using the Adams-Novikov spectral sequence (ANSS), which collapses in this case. At the prime 3, π*(L2V(1)) is also determined by using the ANSS, in which E=E10 in this case. Here V(1) denotes the Toda-Smith 4-cells spectrum. In this paper, we determine the homotopy groups π*(L2V(0)) of the mod 3 Moore spectrum from π*(L2V(1 )) by the Bockstein spectral sequence (BSS). Actually, we first compute the E2-term of the ANSS by the BSS and then study the Adams-Novikov differentials, and obtain E=E10 as well.

Article information

Source
J. Math. Soc. Japan, Volume 52, Number 1 (2000), 65-90.

Dates
First available in Project Euclid: 10 June 2008

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1213107656

Digital Object Identifier
doi:10.2969/jmsj/05210065

Mathematical Reviews number (MathSciNet)
MR1727130

Zentralblatt MATH identifier
0946.55006

Subjects
Primary: 55Q45: Stable homotopy of spheres
Secondary: 55T15: Adams spectral sequences 55Q52: Homotopy groups of special spaces 55P42: Stable homotopy theory, spectra

Keywords
Homotopy groups Adams-Novikov spectral sequence Bousfield-Ravenel localization

Citation

SHIMOMURA, Katsumi. The homotopy groups of the $L_{2}$ -localized mod 3 Moore spectrum. J. Math. Soc. Japan 52 (2000), no. 1, 65--90. doi:10.2969/jmsj/05210065. https://projecteuclid.org/euclid.jmsj/1213107656


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