Stable stems /

Stable stems /

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Bibliographic Details
Author / Creator:	Isaksen, Daniel C., 1972- author.
Imprint:	Providence : American Mathematical Society, [2019] ©2019
Description:	viii, 159 pages : illustrations ; 26 cm.
Language:	English
Series:	Memoirs of the American Mathematical Society, 0065-9266 ; number 1269 Memoirs of the American Mathematical Society ; no. 1269.
Subject:	Homotopy theory. Homotopy groups. Algebraic topology. Algebraic topology. Homotopy groups. Homotopy theory.
Format:	Print Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/12033843

Hidden Bibliographic Details
ISBN:	9781470437886 1470437880
Notes:	"November 2019; Volume 262; number 1269 (sixth of 7 numbers)." Includes bibliographical references (page 151-153) and index.
Summary:	We present a detailed analysis of 2-complete stable homotopy groups, both in the classical context and in the motivic context over C. We use the motivic May spectral sequence to compute the cohomology of the motivic Steenrod algebra over C through the 70-stem. We then use the motivic Adams spectral sequence to obtain motivic stable homotopy groups through the 59-stem. In addition to finding all Adams differentials in this range, we also resolve all hidden extensions by 2, eta, and nu, except for a few carefully enumerated exceptions that remain unknown. The analogous classical stable homotopy groups are easy consequences. We also compute 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. We show that the homotopy groups of the cofiber of tau are the same as the E2-page of the classical Adams-Novikov spectral sequence. This allows us to compute the classical Adams-Novikov spectral sequence, including differentials and hidden extensions, in a larger range than was previously known.

Description
Summary:	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.<br> <br> 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.<br> <br> 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.
Item Description:	"November 2019; Volume 262; number 1269 (sixth of 7 numbers)."
Physical Description:	viii, 159 pages : illustrations ; 26 cm.
Bibliography:	Includes bibliographical references (page 151-153) and index.
ISBN:	9781470437886 1470437880
ISSN:	0065-9266 ;