A NEW FAMILY OF FILTRATION s+6 IN THE STABLE HOMOTOPY GROUPS OF SPHERES

Abstract

In the year 2002, Lin detected a nontrivial family in the stable homotopy groups of spheres π t-6 S which is represented by h n g 0 γ ˜ 3 ∈ Ext A 6 , t ( Z p , Z p ) in the Adams spectral sequence, where t = 2 p n ( p - 1) + 6( p 2 + p + 1)( p - 1) and p ≥ 7 is a prime number. This article generalizes the result and proves the existence of a new nontrivial family of filtration s + 6 in the stable homotopy groups of spheres π t 1- s-6 S which is represented by h n g 0 γ ˜ s + 3 ∈ Ext A s + 6 , t 1 ( Z p , Z p ) in the Adams spectral sequence, where n ≥ 4, 0 ≤ s < p-4, t 1 = 2 p n ( p - 1) + 2( p - 1)(( s + 3) p 2 + ( s + 3) p + ( s + 3)) + s.