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On the E2-term of the bo-Adams spectral sequence

Agnes Beaudry Mark Behrens Prasit Bhattacharya Dominic Culver Zhouli Xu

Algebraic Topology and General Topology mathscidoc:1912.43833

arXiv preprint arXiv:1702.00230
The E_1-term of the (2-local) bo-based Adams spectral sequence for the sphere spectrum decomposes into a direct sum of a v_1-periodic part, and a v_1-torsion part. Lellmann and Mahowald completely computed the d_1-differential on the v_1-periodic part, and the corresponding contribution to the E_2-term. The v_1-torsion part is harder to handle, but with the aid of a computer it was computed through the 20-stem by Davis. Such computer computations are limited by the exponential growth of v_1-torsion in the E_1-term. In this paper, we introduce a new method for computing the contribution of the v_1-torsion part to the E_2-term, whose input is the cohomology of the Steenrod algebra. We demonstrate the efficacy of our technique by computing the bo-Adams spectral sequence beyond the 40-stem.
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@inproceedings{agneson,
  title={On the E2-term of the bo-Adams spectral sequence},
  author={Agnes Beaudry, Mark Behrens, Prasit Bhattacharya, Dominic Culver, and Zhouli Xu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210101718108397},
  booktitle={arXiv preprint arXiv:1702.00230},
}
Agnes Beaudry, Mark Behrens, Prasit Bhattacharya, Dominic Culver, and Zhouli Xu. On the E2-term of the bo-Adams spectral sequence. In arXiv preprint arXiv:1702.00230. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210101718108397.
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