On the E2‐term of the bo‐Adams spectral sequence. Issue 1 (11th January 2020)

• Record Type: Journal Article
• Authors: Beaudry, A.; Behrens, M.; Bhattacharya, P.; Culver, D.; Xu, Z.
• Is Part Of: Journal of topology. Volume 13:Issue 1(2020)
• Page Start: 356
• Page End: 415
• Publication Date: 2020-01-11
• Subjects: 55Q45 -- 55T15 (primary); Topology -- Periodicals; 514.05
• DOI: 10.1112/topo.12136
• Languages: English
• ISSNs: 1753-8416

Abstract

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.