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The homotopy groups of $ L_2T(1)/(v_1)$ at an odd prime


Authors: Liu Xiugui, Wang Xiangjun and Yuan Zihong
Journal: Proc. Amer. Math. Soc. 138 (2010), 1143-1152
MSC (2000): Primary 55Q99, 55Q52
DOI: https://doi.org/10.1090/S0002-9939-09-10138-7
Published electronically: October 28, 2009
MathSciNet review: 2566579
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Abstract: In this paper, all spectra are localized at an odd prime. Let $ T(1)$ be the Ravenel spectrum characterized by $ BP_{\ast}$-homology as $ BP_{\ast}[t_1]$, $ T(1)/(v_1)$ be the cofiber of the self-map $ v_1: \Sigma^{2p-2}T(1)\rightarrow T(1)$ and $ L_2$ denote the Bousfield localization functor with respect to $ v_2^{-1}BP_{\ast}$. In this paper, we determine the homotopy groups of $ L_2T(1)/(v_1)$.


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Additional Information

Liu Xiugui
Affiliation: School of Mathematical Science and LPMC, Nankai University, Tianjin 300071, People’s Republic of China

Wang Xiangjun
Affiliation: School of Mathematical Science and LPMC, Nankai University, Tianjin 300071, People’s Republic of China

Yuan Zihong
Affiliation: School of Mathematical Science and LPMC, Nankai University, Tianjin 300071, People’s Republic of China
Email: yuanzhchina@gmail.com

DOI: https://doi.org/10.1090/S0002-9939-09-10138-7
Keywords: Stable homotopy, Adams-Novikov spectral sequence, chromatic spectral sequence
Received by editor(s): August 1, 2008
Received by editor(s) in revised form: July 22, 2009
Published electronically: October 28, 2009
Additional Notes: The authors were partially supported by NSFC grant No. 10771105.
Communicated by: Paul Goerss
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.