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Description of  Stable Stems (Memoirs of the American Mathematical Society)

1470437880 pdf "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 alsocompute 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" Read more