Geodesic
A Product Involving the β-Family in Stable Homotopy Theory
Bulletin of the Malaysian Mathematical Society, Tome 33 (2010) no. 3 Cet article a éte moissonné depuis la source Bulletin of the Malaysian Mathematical Society website

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In the stable homotopy groups π q ( p n + p m +1)-3 ( S ) of the sphere spectrum S localized at the prime p greater than three, J. Lin constructed an essential family ξ m,n for n ≥ m + 2 > 5. In this paper, the authors show that the composite ξ m,n β s ∈ π q ( p n + p m + sp + s )-5 ( S ) for 2 ≤ s p is non-trivial, where q = 2( p - 1) and β s ∈ π q ( sp + s -1)-2 ( S ) is the known β -family. We show our result by explicit combinatorial analysis of the (modified) May spectral sequence.
Classification : 55Q45, 55T15. 
@article{BMMS_2010_33_3_a6,
     author = {Xiugui Liu and Wending Li},
     title = {A {Product} {Involving} the {\ensuremath{\beta}-Family} in {Stable} {Homotopy} {Theory}},
     journal = {Bulletin of the Malaysian Mathematical Society},
     year = {2010},
     volume = {33},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/BMMS_2010_33_3_a6/}
}
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Xiugui Liu; Wending Li. A Product Involving the β-Family in Stable Homotopy Theory. Bulletin of the Malaysian Mathematical Society, Tome 33 (2010) no. 3. http://geodesic.mathdoc.fr/item/BMMS_2010_33_3_a6/