Volume 6, Issue 4, August 2017, Page: 196-201
A Nontrivial Product in the Stable Homotopy of Spheres
Wang Chong, College of Mathematical and Statistics, Cangzhou Normal University, Cangzhou, China
Received: Aug. 7, 2017;       Published: Aug. 7, 2017
DOI: 10.11648/j.acm.20170604.17      View  333      Downloads  30
Abstract
Let  be an arbitrary odd prime number greater than eleven andbe the mod  Steenrod algebra. In this paper, it has proved that the product  is nontrivial and converges to  nontrivially of order  in , where , by making use of the Adams spectral sequence.
Keywords
Steenrod Algebra, Cohomology, May Spectral Sequence, Stable Homotopy of Spheres
To cite this article
Wang Chong, A Nontrivial Product in the Stable Homotopy of Spheres, Applied and Computational Mathematics. Vol. 6, No. 4, 2017, pp. 196-201. doi: 10.11648/j.acm.20170604.17
Reference
[1]
Cohen R. L., Odd primary families in stable homotopy theory, Mem. Amer. Math. S oc., 1981, 242: 1-92.
[2]
J. F.Adams,Stable Homotopy and Generalised Homology, Chicago: University of Chicago Press, 1974.
[3]
A. Liulevicius, The factorizations of cyclic reduced powersbysecondary cohomology operations, Mem. Amer. Math. Soc. 42 1962:1-112.
[4]
Miller H. R., Ravenel D. C. and Wilson W. S., Periodic phenome-na in the Adams-Novikov spectral sequence, Ann. of Math., 1977, 106:469-516.
[5]
T. Aikawa, 3-dimensional cohomology of the modSteenrod algebra, Math. Scand. 47 (1980), 91--115.
[6]
X. Liu and H. Zhao, On a product in the classical Adams spectral sequence, Proc. Amer. Math. Soc. 137 (2009), no. 7, 2489-2496.
[7]
X. Wang and Q. Zheng, The convergence of , Sci. China Ser. A 41 (1998), no. 6, 622-628.
[8]
D. C. Ravenel, Complex Cobordism and Stable Homotopy Groups of Spheres, Orlando: Academic Press, 1986.
[9]
X. Liu, Some infinite elements in the Adams spetral sequence for the sphere spectrum, J. Math. Kyoto Univ.48 (2008), 617-629.
[10]
Hao Zhao, Xiangjun Wang, Linan Zhong. The convergence of the product  in the Adams spectral sequence. Forum Mathematicum, 2015, 27 (3):1613-1637.
[11]
Zhong Linan, X. Liu. Non-Triviality of the Product in the Adams Spectral Sequence. Acta Mathematica Scientia, 2014, 34 (2):274-282.
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