Stable stems
Author(s)
Bibliographic Information
Stable stems
（Memoirs of the American Mathematical Society, no. 1269）
American Mathematical Society, c2019
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Note
"November 2019, volume 262, number 1269 (sixth of 7 numbers)"
Includes bibliographical reference (p. 151-153) and index
Description and Table of Contents
Description
The author presents a detailed analysis of 2-complete stable homotopy groups, both in the classical context and in the motivic context over $\mathbb C$. He uses the motivic May spectral sequence to compute the cohomology of the motivic Steenrod algebra over $\mathbb C$ through the 70-stem. He then uses the motivic Adams spectral sequence to obtain motivic stable homotopy groups through the 59-stem. He also describes the complete calculation to the 65-stem, but defers the proofs in this range to forthcoming publications.
In addition to finding all Adams differentials, the author also resolves all hidden extensions by $2$, $\eta $, and $\nu $ through the 59-stem, except for a few carefully enumerated exceptions that remain unknown. The analogous classical stable homotopy groups are easy consequences.
The author also computes the motivic stable homotopy groups of the cofiber of the motivic element $\tau $. This computation is essential for resolving hidden extensions in the Adams spectral sequence. He shows that the homotopy groups of the cofiber of $\tau $ are the same as the $E_2$-page of the classical Adams-Novikov spectral sequence. This allows him to compute the classical Adams-Novikov spectral sequence, including differentials and hidden extensions, in a larger range than was previously known.
Table of Contents
Introduction
The cohomology of the motivic Steenrod algebra
Differentials in the Adams spectral sequence
Hidden extensions in the Adams spectral sequence
The cofiber of $\tau $
Reverse engineering the Adams-Novikov spectral sequence
Tables
Bibliography
Index.
by "Nielsen BookData"
