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010 a| 2020023141;

020 a| 9781470437886q| (paperback);

020 z| 9781470455125q| (ebook);

035 a| (WaSeSS)ssj0002408401;

042 a| pcc;

049 a| EREEa| NEHH;

050 00 a| QA612.7b| .I73 2019;

082 00 a| 514/.242| 23;

084 a| 14F42a| 55Q45a| 55S10a| 55T15a| 16T05a| 55P42a| 55Q10a| 55S302| msc;

100 1 a| Isaksen, Daniel C.,d| 1972-=| ^A796740;

245 10 a| Stable stemsh| [electronic resource] /c| Daniel C. Isaksen.;

260 a| Providence :b| American Mathematical Society,c| [2019];

300 a| viii, 159 pages :b| illustrations ;c| 26 cm.;

504 a| Includes bibliographical references (page 151-153) and index.;

506 a| Available only to authorized users.;

520 a| "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. We also describe the complete calculation to the 65-stem, but defer the proofs in this range to forthcoming publications. In addition to finding all Adams differentials, we also resolve all hidden extensions by 2, n, 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. We also compute the motivic stable homotopy groups of the cofiber of the motivic element t. 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"--c| Provided by publisher.;

538 a| Mode of access: World Wide Web;

650 0 a| Homotopy theory.=| ^A18132;

650 0 a| Algebraic topology.=| ^A22632;

650 7 a| Algebraic geometry -- (Co)homology theory [See also 13Dxx] -- Motivic cohomology; motivic homotopy theory [See also 19E15].2| msc;

650 7 a| Algebraic topology -- Homotopy groups -- Stable homotopy of spheres.2| msc;

650 7 a| Algebraic topology -- Operations and obstructions -- Steenrod algebra.2| msc;

650 7 a| Algebraic topology -- Spectral sequences [See also 18G40, 55R20] -- Adams spectral sequences.2| msc;

650 7 a| Associative rings and algebras {For the commutative case, see 13-XX} -- Hopf algebras, quantum groups and related topics -- Hopf algebras and their applications [See also 16S40, 57T05].2| msc;

650 7 a| Algebraic topology -- Homotopy theory {For simple homotopy type, see 57Q10} -- Stable homotopy theory, spectra.2| msc;

650 7 a| Algebraic topology -- Homotopy groups -- Stable homotopy groups.2| msc;

650 7 a| Algebraic topology -- Operations and obstructions -- Massey products.2| msc;

655 0 a| Electronic books.=| ^A491897;

856 40 z| Full text available from Ebook Central - Academic Completeu| https://ebookcentral.proquest.com/lib/eastcarolina/detail.action?docID=6118462;

949 a| CLICK ON WEB ADDRESSw| ASISh| JOYNER188;

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999 a| CLICK ON WEB ADDRESSw| ASISc| 1i| 5656140-2001l| HSLELECm| HSLr| Ys| Yt| HEBKu| 7/21/2021x| EBOOKz| HERESOURCE;

999 a| CLICK ON WEB ADDRESSw| ASISc| 1i| 5656140-3001l| MNETm| JMUSICr| Ys| Yt| MNESSBKu| 7/21/2021x| EBOOKz| JERESOURCE;

Stable stems / Daniel C. Isaksen.

Author/creator	Isaksen, Daniel C., 1972-
Format	Electronic
Publication Info	Providence : American Mathematical Society, [2019]
Description	viii, 159 pages : illustrations ; 26 cm.
Supplemental Content	Full text available from Ebook Central - Academic Complete
Subjects	Homotopy theory. Algebraic topology.

Abstract	"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. We also describe the complete calculation to the 65-stem, but defer the proofs in this range to forthcoming publications. In addition to finding all Adams differentials, we also resolve all hidden extensions by 2, n, 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. We also compute the motivic stable homotopy groups of the cofiber of the motivic element t. 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"-- Provided by publisher.
Bibliography note	Includes bibliographical references (page 151-153) and index.
Access restriction	Available only to authorized users.
Technical details	Mode of access: World Wide Web
Genre/form	Electronic books.
LCCN	2020023141
ISBN	9781470437886 (paperback)
ISBN	(ebook)

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