Periodic phenomena in the classical Adams spectral sequence

Mahowald, Mark; Shick, Paul

doi:10.1090/S0002-9947-1987-0871672-0

Periodic phenomena in the classical Adams spectral sequence
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by Mark Mahowald and Paul Shick PDF

Trans. Amer. Math. Soc. 300 (1987), 191-206 Request permission

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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Ext over the subalgebra

of the Steenrod algebra for stunted projected spaces

2

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