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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Periodic phenomena in the classical Adams spectral sequence


Authors: Mark Mahowald and Paul Shick
Journal: Trans. Amer. Math. Soc. 300 (1987), 191-206
MSC: Primary 55T15; Secondary 55N22, 55Q45, 55S10
MathSciNet review: 871672
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Abstract: We investigate certain periodic phenomena in the classical Adams sepctral sequence which are related to the polynomial generators $ {\nu _n}$ in $ {\pi _{\ast}}(\operatorname{BP} )$. We define the notion of a class $ a$ in $ {\operatorname{Ext} _A}({\mathbf{Z}}/2,{\mathbf{Z}}/2)$ being $ {\nu _n}$-periodic or $ {\nu _n}$-torsion and prove that classes that are $ {\nu _n}$-torsion are also $ {\nu _k}$-torsion for all $ k$ such that $ 0 \leqslant k \leqslant n$. This allows us to define a chromatic filtration of $ {\operatorname{Ext} _A}({\mathbf{Z}}/2,{\mathbf{Z}}/2)$ paralleling the chromatic filtration of the Novikov spectral sequence $ {E_2}$-term given in [13].


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DOI: http://dx.doi.org/10.1090/S0002-9947-1987-0871672-0
PII: S 0002-9947(1987)0871672-0
Article copyright: © Copyright 1987 American Mathematical Society