Acta mathematica scientia, Series B >
SOME NEW FAMILIES OF FILTRATION FIVE IN THE STABLE HOMOTOPY OF SPHERES
Received date: 2006-12-30
Revised date: 2007-08-30
Online published: 2009-09-20
Supported by
Supported by NSFC (10171049)
This study proves a general result on convergence of α2 x ∈ ExtAs+2, tq+2q+1(Zp, Zp) in the Adams spectral sequence and as a consequence, the study detects some new families in the stable homotopy groups of spheres πtq+2q-4S which is represented in the Adams spectral sequence by α2fn, α2f'n, ，α2huhmhn ∈ ExtA5, tq+2q+1(Zp, Zp) with tq = pn+1q+2pnq, 2pn+1q+pnq, puq+pmq+pnq, respectively, where α2 ∈Exta2, 2q+1Zp, Zp), fn ∈ ExtA3, pn+1q+2pnq(Zp, Zp), f'n ∈ ExtA3, 2pn+1q+pnq (Zp, Zp), hn ∈ ExtA1,pnq(Zp, Zp) and p ≥ 5 is a prime, q = 2(p-1), n ≥ 2.
LIN Jin-Kun . SOME NEW FAMILIES OF FILTRATION FIVE IN THE STABLE HOMOTOPY OF SPHERES[J]. Acta mathematica scientia, Series B, 2009 , 29(5) : 1395 -1404 . DOI: 10.1016/S0252-9602(09)60112-0
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