An extension in the Adams spectral sequence in dimension 54
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.
- Publication:
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arXiv e-prints
- Pub Date:
- May 2020
- DOI:
- 10.48550/arXiv.2005.08910
- arXiv:
- arXiv:2005.08910
- Bibcode:
- 2020arXiv200508910B
- Keywords:
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- Mathematics - Algebraic Topology
- E-Print:
- 3 pages. Comments welcome!