Some products involving the fourth Greek letter family element \tilde{d}s in the Adams spectral sequence

Authors : Xiugui LIU

Pages : 311-321

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Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :Let p be an odd prime and A be the mod p Steenrod algebra. For computing the stable homotopy groups of spheres with the classical Adams spectral sequence, we must compute the E2-term of the Adams spectral sequence, ExtA\ast,\ast insert ignore into journalissuearticles values(Zp,Zp);. In this paper we prove that in the cohomology of A, the product k0 hn \tilde d s + 4 \in ExtAs + 7, tinsert ignore into journalissuearticles values(s,n); + s insert ignore into journalissuearticles values(Zp, Zp);, is nontrivial for n \geq 5, and trivial for n=3, 4, where \tildeds + 4 is actually \tildeas + 4insert ignore into journalissuearticles values(4); described by Wang and Zheng, p \geq 11, 0 \leq s < p - 4 and tinsert ignore into journalissuearticles values(s,n);=2insert ignore into journalissuearticles values(p-1);[insert ignore into journalissuearticles values(s + 2); + insert ignore into journalissuearticles values(s + 4);p + insert ignore into journalissuearticles values(s + 3);p2 + insert ignore into journalissuearticles values(s + 4);p3 + pn].
Keywords : Key words Steenrod algebra, cohomology, Adams spectral sequence, May spectral sequence