A pull back theorem in the Adams spectral sequence |
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| Authors: | Jin Kun Lin |
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| Institution: | (1) School of Mathematical Science and LPMC, Nankai University, Tianjin, 300071, P. R. China |
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| Abstract: | This paper proves that, for any generator x ε Ext
A
s,tq
(Z
p
, Z
p
), if (1
L
⋀ i)*φ*(x) ε Ext
A
s+1,tq+2q
(H*L ⋀ M,Z
p
) is a permanent cycle in the Adams spectral sequence (ASS), then h0x ε Ext
A
s+1,tq+q
(Z
p
, Z
p
) also is a permenent cycle in the ASS. As an application, the paper obtains that h
0
h
n
h
m
∈  is a permanent cycle in the ASS and it converges to elements of order p in the stable homotopy groups of spheres  , where p ≥ 5 is a prime, s ≤ 4, n ≥ m+2 ≥ 4 and M is the Moore spectrum.
Supported by NSFC No. 10171049 |
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| Keywords: | Adams spectral sequence Toda spectrum stable homotopy groups of spheres |
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