Beta families arising from a \(v_2^9\) self-map on \(S/(3, v_1^8)\)

DOI10.2140/agt.2023.23.4349arXiv2109.01059OpenAlexW4389099861MaRDI QIDQ6065488

Katsumi Shimomura, Eva Belmont

Publication date: 11 December 2023

Published in: Algebraic \& Geometric Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2109.01059

zbMATH Keywords

Adams-Novikov spectral sequence\(v_2\)-periodicity\(\operatorname{tmf}\)

Mathematics Subject Classification ID

Generalized cohomology and spectral sequences in algebraic topology (55T25) Stable homotopy of spheres (55Q45) (v_n)-periodicity (55Q51)

Cites Work

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• The beta elements \(\beta_{tp^2/r}\) in the homotopy of spheres
• Periodic phenomena in the Adams-Novikov spectral sequence
• Computations of the Adams-Novikov \(E_2\)-term
• The homotopy of the \(K(2)\)-local Moore spectrum at the prime 3 revisited
• On spectra realizing exterior parts of the Steenrod algebra
• Stable homotopy over the Steenrod algebra
• The homotopy groups of 𝑡𝑚𝑓 and of its localizations
• Note on beta elements in homotopy, and an application to the prime three case
• NOTE ON THE β-FAMILY IN STABLE HOMOTOPY OF SPHERES AT THE PRIME 3
• The non-existence of odd primary Arf invariant elements in stable homotopy
• The homotopy groups of the 𝐿₂-localized Toda-Smith spectrum 𝑉(1) at the prime 3
• The 2-primary Hurewicz image of \(\operatorname{tmf}\)

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