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On the E2‐term of the bo‐Adams spectral sequence
Journal of Topology ( IF 0.8 ) Pub Date : 2020-01-11 , DOI: 10.1112/topo.12136
A. Beaudry 1 , M. Behrens 2 , P. Bhattacharya 3 , D. Culver 4 , Z. Xu 5
Affiliation  

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.

中文翻译:

关于bo-Adams光谱序列的E2项

Ë 1个 (2-本地)的术语 基于球面光谱的Adams光谱序列分解为a的直接和 v 1个 周期部分,以及 v 1个 扭转部分。Lellmann和Mahowald完全计算了 d 1个 -在 v 1个 周期部分,以及对 Ë 2 -术语。的 v 1个 扭转零件较难处理,但借助计算机,它是由戴维斯(Davis)通过20杆计算的。此类计算机计算受到以下因素的指数增长的限制: v 1个 扭转 Ë 1个 -术语。在本文中,我们介绍了一种新的方法来计算 v 1个 扭转部分 Ë 2 -term,其输入是Steenrod代数的同调性。我们通过计算 -40根以外的亚当光谱序列。
更新日期:2020-01-11
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