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Motivic stable homotopy and the stable 51 and 52 stems

Daniel C Isaksen Zhouli Xu

Algebraic Topology and General Topology mathscidoc:1912.43831

Topology and its Applications, 190, 31-34, 2015.8
We establish a differential d 2 (D 1)= h 0 2 h 3 g 2 in the 51-stem of the Adams spectral sequence at the prime 2, which gives the first correct calculation of the stable 51 and 52 stems. This differential is remarkable since we know of no way to prove it without recourse to the motivic Adams spectral sequence. It is the last undetermined differential in the range of the first author's detailed calculations of the n-stems for n< 60 [6]. This note advertises the use of the motivic Adams spectral sequence to obtain information about classical stable homotopy groups.
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@inproceedings{daniel2015motivic,
  title={Motivic stable homotopy and the stable 51 and 52 stems},
  author={Daniel C Isaksen, and Zhouli Xu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210055220503395},
  booktitle={Topology and its Applications},
  volume={190},
  pages={31-34},
  year={2015},
}
Daniel C Isaksen, and Zhouli Xu. Motivic stable homotopy and the stable 51 and 52 stems. 2015. Vol. 190. In Topology and its Applications. pp.31-34. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210055220503395.
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