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arXiv · 2005.08910

An extension in the Adams spectral sequence in dimension 54

Robert Burklund
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Abstract

We establish a hidden extension in the Adams spectral sequence converging to the stable homotopy groups of spheres at the prime 2 in the 54-stem. This extension is exceptional in that the only proof we know proceeds via Pstragowski's category of synthetic spectra. This was the final unresolved hidden 2-extension in the Adams spectral sequence through dimension 80. We hope this provides a concise demonstration of the computational leverage provided by $\mathbb{F}_2$-synthetic spectra.

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Robert Burklund. 2020-05-18. An extension in the Adams spectral sequence in dimension 54. https://doi.org/10.1112/blms.12428

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