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On Root Invariants Of Periodic Classes In Exta(Z/2,Z/2), Paul L. Shick
On Root Invariants Of Periodic Classes In Exta(Z/2,Z/2), Paul L. Shick
Mathematics and Computer Science
We prove that if a class in the cohomology of the mod 2 Steenrod algebra is υn-periodic in the sense of [10[, then its root invariant must be υn+1-periodic, where υn denotes the nth generator of π∗(ΒΡ).
Periodic Phenomena In The Classical Adams Spectral Sequence, Mark Mahowald, Paul L. Shick
Periodic Phenomena In The Classical Adams Spectral Sequence, Mark Mahowald, Paul L. Shick
Mathematics and Computer Science
We investigate certain periodic phenomena in the classical Adams spectral sequence which are related to the polynomial generators υn in π∗(ΒΡ). We define the notion of a class α in ExtΑ(Ζ/2,Ζ/2) being υn-periodic or υn-torsion and prove that classes that are υn-torsion are also υκ-torsion for all κ such that 0 ≤ κ ≤ n. This allows us to define a chromatic filtration of ExtΑ(Ζ/2,Ζ/2) paralleling the chromatic filtration of the Novikov spectral sequence Ε2-term …