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Let A be the mod p Steenrod algebra for p an arbitrary oddprime and S the sphere spectrum localized at p. In this paper,some useful propositions about the May spectral sequence are firstgiven, and then, two new nontrivial homotopy elements alpha_1jxi_n (pgeq 5,ngeq 3) and gamma_salpha_1 jxi_n(pgeq 7, ngeq 4) are detected in the stable homotopy groupsof spheres, where xi_nin pi_{p^nq+pq-2}M is obtained in [2].The new ones are of degree 2(p-1)(p^n+p+1)-4 and2(p-1)(p^n+sp^2+sp+(s-1))-7 and are represented up to nonzeroscalar by b_0h_0h_n, b_0 h_0 h_n tilde{gamma}_{s}not=0inoperatorname{Ext}_A^{ast,ast}(Z_p,Z_p) in the Adams spectralsequence respectively, where 3leq s<p-2.
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참고문헌 (9)
참고문헌 신청
/ 1977 / Periodic phenomena in the Adams-Novikov spectral sequence : 469 ~
/ 1981 / Odd primary families in stable homotopy theory 30 (242) : 92 ~
/ 1986. / Complex cobordism and stableHomotopy groups of spheres
/ 1989. / Lecture Notes in Mathematics. No. 1370
/ 1995 / Ordered cochain complex and H^{4,ast(A_p) for pgeq 5} 1 : 80 ~ 99
/ 1981 / Odd primary families in stable homotopy theory 30 (242) : 92 ~
/ 1986. / Complex cobordism and stableHomotopy groups of spheres
/ 1989. / Lecture Notes in Mathematics. No. 1370
/ 1995 / Ordered cochain complex and H^{4,ast(A_p) for pgeq 5} 1 : 80 ~ 99
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