Stable stems
著者
書誌事項
Stable stems
(Memoirs of the American Mathematical Society, no. 1269)
American Mathematical Society, c2019
大学図書館所蔵 全7件
  青森
  岩手
  宮城
  秋田
  山形
  福島
  茨城
  栃木
  群馬
  埼玉
  千葉
  東京
  神奈川
  新潟
  富山
  石川
  福井
  山梨
  長野
  岐阜
  静岡
  愛知
  三重
  滋賀
  京都
  大阪
  兵庫
  奈良
  和歌山
  鳥取
  島根
  岡山
  広島
  山口
  徳島
  香川
  愛媛
  高知
  福岡
  佐賀
  長崎
  熊本
  大分
  宮崎
  鹿児島
  沖縄
  韓国
  中国
  タイ
  イギリス
  ドイツ
  スイス
  フランス
  ベルギー
  オランダ
  スウェーデン
  ノルウェー
  アメリカ
注記
"November 2019, volume 262, number 1269 (sixth of 7 numbers)"
Includes bibliographical reference (p. 151-153) and index
内容説明・目次
内容説明
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.
目次
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.
「Nielsen BookData」 より