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Nonvanishing of products in $v_2$-periodic families at the prime $3$
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abstract
Many products amongst $v_2$-periodic families in the stable homotopy groups of spheres are shown not to vanish and some Toda brackets are shown not to contain zero. This is done by carefully studying the action of Adams operations on topological modular forms. A crucial ingredient is Pstragowski's category of synthetic spectra which affords us the necessary freedom to work with (modified) Adams--Novikov spectral sequences.
Forward citations
Cited by 2 Pith papers
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On periodic families in the stable stems of height two
Theorem A establishes 125 nonzero v_2^32-periodic families in the 2-primary stable stems, 50 new, all vanishing in TMF yet detected by the Atkin-Lehner fixed point spectrum J_0(3).
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Revisiting the $\beta_1$-action on the $3$-primary stable homotopy groups of spheres
Products of the 3-primary β₁-periodic family in the stable homotopy groups of spheres are nonzero for up to five factors and zero for six or more, with analogous sharp cutoffs for β₂-, α₁β₂-, and [α₁β₃/3]-twisted products.
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