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On a product in the classical Adams spectral sequence


Authors: Xiugui Liu and Hao Zhao
Journal: Proc. Amer. Math. Soc. 137 (2009), 2489-2496
MSC (2000): Primary 55Q45
DOI: https://doi.org/10.1090/S0002-9939-09-09809-8
Published electronically: February 11, 2009
MathSciNet review: 2495286
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Abstract: In this paper, we prove the nontriviality of the product $ h_0b_0\tilde{\delta}_s\in {\rm Ext}_A^{s+3,t(s)}(\mathbb{Z}_p,\mathbb{Z}_p)$ in the classical Adams spectral sequence, where $ p\geq 11$, $ 4\leq s<p$, $ t(s)=2(p-1)[sp^3+(s-1)p^2+(s-1)p+(s-2)]+(s-4)$ and $ \tilde{\delta}_s$ was obtained by X. Wang and Q. Zheng.


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Additional Information

Xiugui Liu
Affiliation: School of Mathematical Sciences and Laboratory of Pure Mathematics and Combinatorics, Nankai University, Tianjin 300071, People’s Republic of China
Email: xgliu@nankai.edu.cn, matlxg@hotmail.com

Hao Zhao
Affiliation: School of Mathematics, The University of Manchester, Oxford Road, Manchester, M13 9PL, United Kingdom
Email: Hao.Zhao@manchester.ac.uk

DOI: https://doi.org/10.1090/S0002-9939-09-09809-8
Keywords: Stable homotopy groups of spheres, Adams spectral sequence, May spectral sequence
Received by editor(s): September 3, 2008
Received by editor(s) in revised form: October 16, 2008
Published electronically: February 11, 2009
Additional Notes: The first author was supported in part by the National Natural Science Foundation of China (Nos. 10501045, 10771105) and the Fund of the Personnel Division of Nankai University.
Communicated by: Paul Goerss
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.