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OverviewThe 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. Full Product DetailsAuthor: Daniel C. IsaksenPublisher: American Mathematical Society Imprint: American Mathematical Society Weight: 0.333kg ISBN: 9781470437886ISBN 10: 1470437880 Pages: 161 Publication Date: 30 June 2020 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: In Print This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsIntroduction 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.ReviewsAuthor InformationDaniel C. Isaksen, Wayne State University, Detroit, MI. Tab Content 6Author Website:Countries AvailableAll regions |