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| SOME NEW FAMILIES OF FILTRATION FOUR IN THE STABLE HOMOTOPY OF SPHERES |
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Citation： |
LIN Jinkun.SOME NEW FAMILIES OF FILTRATION FOUR IN THE STABLE HOMOTOPY OF SPHERES[J].Chinese Annals of Mathematics B,1999,20(1):93~102 |
| Page view： 1063
Net amount： 624 |
Authors： |
LIN Jinkun; |
Foundation： |
the National Natural Science Foundation of China (No. 19531040) |
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| Abstract： |
This paper proves the existence of 4 families of nontrivial homotopy elements in the stable homotopy of spheres which are represented by $\alpha_{2} b_{n}$,$\alpha_{2}k_{n}$, $\alpha_{2}g_{n}$ and $\alpha_{2}h_{n}h_{m}$ in the
$E_{2}^{4,*}$-terms of the Adams spectral sequence respectively, where $\alpha_{2}$, $b_{n}$, $k_{n}$, $g_{n}$
and $h_{n}h_{m}$ are the known generators in the $E_{2}^{2,*}$-terms whose internal degree are $4(p-1)+1$, $2p^{n+1}(p-1)$,
$(4p^{n+1}+2p^{n})(p-1)$,$(2p^{n+1}+4p^{n})(p-1)$, $(2p^{n}+2p^{m})(p-1)$ respectively and $p \geq 5$ is a prime, $m\geq n+2 \geq 4$. |
Keywords： |
Stable homotopy of spheres, Adams spectral sequence,
Derivations of maps, M-module spectra |
Classification： |
55Q45 |
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