The Convergence of $\widetilde{\gamma }_{s} {\left( {b_{0} h_{n} - h_{1} b_{{n - 1}} } \right)}$*

Abstract

This paper computes the Thom map on γ₂ and proves that it is represented by 2b _2,0 h _1,2 in the ASS. The authors also compute the higher May differential of b _2,0, from which it is proved that $\widetilde{\gamma }_{s} {\left( {b_{0} h_{n} - h_{1} b_{{n - 1}} } \right)}$ for 2 ≤ s < p - 1 are permanent cycles in the ASS.

Keywords

Stable homotopy / Adams spectral sequence / May spectral sequence / 5Q52 / 55Q40

References

[1] Adams, J. F., Stable Homotopy and Generalised Homology, University of Chicago Press, Chicago, 1974.

[2] Aikawa Math. Scand., 1980, 47: 91

[3] Cohen, R., Odd Primary Infinite Families in Stable Homotopy Theory, Memoirs of A. M. S., 42, 1981.

[4] Lin Hiroshima Math. J., 2001, 31: 477

[5] Liulevicius, A., The Factorization of Cyclic Reduced Powers by Secondary Cohomology Operations, Memoirs of A. M. S., 42, 1962.

[6] May J. Algebra, 1966, 3: 123

[7] Ravenel, D. C., Complex Cobordism and Stable Homotopy Groups of Spheres, Academic Press, New York, 1986.

[8] Shimomura Topology, 1995, 34: 261

[9] Toda Topology, 1971, 10: 55

[10] Wang Science in China, 1998, 41: 622

[11] Zhou, X., Higher Cohomology Operations That Detect Homotopy Theory, Lecture Notes in Math., 1370, 416-436.