Please enter verification code
Special Issues
A Nontrivial Product in the Stable Homotopy of Spheres
Applied and Computational Mathematics
Volume 6, Issue 4, August 2017, Pages: 196-201
Received: Aug. 7, 2017; Published: Aug. 7, 2017
Views 2276      Downloads 99
Wang Chong, College of Mathematical and Statistics, Cangzhou Normal University, Cangzhou, China
Article Tools
Follow on us
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.
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
Cohen R. L., Odd primary families in stable homotopy theory, Mem. Amer. Math. S oc., 1981, 242: 1-92.
J. F.Adams,Stable Homotopy and Generalised Homology, Chicago: University of Chicago Press, 1974.
A. Liulevicius, The factorizations of cyclic reduced powersbysecondary cohomology operations, Mem. Amer. Math. Soc. 42 1962:1-112.
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.
T. Aikawa, 3-dimensional cohomology of the modSteenrod algebra, Math. Scand. 47 (1980), 91--115.
X. Liu and H. Zhao, On a product in the classical Adams spectral sequence, Proc. Amer. Math. Soc. 137 (2009), no. 7, 2489-2496.
X. Wang and Q. Zheng, The convergence of , Sci. China Ser. A 41 (1998), no. 6, 622-628.
D. C. Ravenel, Complex Cobordism and Stable Homotopy Groups of Spheres, Orlando: Academic Press, 1986.
X. Liu, Some infinite elements in the Adams spetral sequence for the sphere spectrum, J. Math. Kyoto Univ.48 (2008), 617-629.
Hao Zhao, Xiangjun Wang, Linan Zhong. The convergence of the product  in the Adams spectral sequence. Forum Mathematicum, 2015, 27 (3):1613-1637.
Zhong Linan, X. Liu. Non-Triviality of the Product in the Adams Spectral Sequence. Acta Mathematica Scientia, 2014, 34 (2):274-282.
Science Publishing Group
1 Rockefeller Plaza,
10th and 11th Floors,
New York, NY 10020
Tel: (001)347-983-5186