Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

On a product in the classical Adams spectral sequence
HTML articles powered by AMS MathViewer

by Xiugui Liu and Hao Zhao PDF
Proc. Amer. Math. Soc. 137 (2009), 2489-2496 Request permission

Abstract:

In this paper, we prove the nontriviality of the product $h_0b_0\tilde {\delta }_s\in \textrm {Ext}_A^{s+3,t(s)}(\mathbb {Z}_p,\mathbb {Z}_p)$ 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.
References
  • J. F. Adams, Stable homotopy and generalised homology, Chicago Lectures in Mathematics, University of Chicago Press, Chicago, Ill.-London, 1974. MR 0402720
  • Tetsuya Aikawa, $3$-dimensional cohomology of the mod $p$ Steenrod algebra, Math. Scand. 47 (1980), no. 1, 91–115. MR 600080, DOI 10.7146/math.scand.a-11876
  • Xiugui Liu, A nontrivial product in the stable homotopy groups of spheres, Sci. China Ser. A 47 (2004), no. 6, 831–841. MR 2127211, DOI 10.1360/03ys0111
  • X. Liu, On two non-trivial products in the stable homotopy groups of spheres, Bol. Soc. Mat. Mexicana(3) 13 (2007), 367–380.
  • X. Liu, Some infinite elements in the Adams spectral sequence for the sphere spectrum, J. Math. Kyoto Univ. 48 (2008), 617–629.
  • Arunas Liulevicius, The factorization of cyclic reduced powers by secondary cohomology operations, Mem. Amer. Math. Soc. 42 (1962), 112. MR 182001
  • Douglas C. Ravenel, Complex cobordism and stable homotopy groups of spheres, Pure and Applied Mathematics, vol. 121, Academic Press, Inc., Orlando, FL, 1986. MR 860042
  • Xiangjun Wang and Qibing Zheng, The convergence of $\tilde \alpha _s^{(n)}h_0h_k$, Sci. China Ser. A 41 (1998), no. 6, 622–628. MR 1633827, DOI 10.1007/BF02876232
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 55Q45
  • Retrieve articles in all journals with MSC (2000): 55Q45
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
  • 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
  • © Copyright 2009 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 137 (2009), 2489-2496
  • MSC (2000): Primary 55Q45
  • DOI: https://doi.org/10.1090/S0002-9939-09-09809-8
  • MathSciNet review: 2495286