On the E2-term of the bo-Adams spectral sequence
Abstract
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.
Keywords
Cite
@article{arxiv.1702.00230,
title = {On the E2-term of the bo-Adams spectral sequence},
author = {Agnes Beaudry and Mark Behrens and Prasit Bhattacharya and Dominic Culver and Zhouli Xu},
journal= {arXiv preprint arXiv:1702.00230},
year = {2020}
}
Comments
64 pages, 16 figures, few minor typos fixed, accepted to J. Topology