Stable stems / Daniel C. Isaksen.

Format:

Book

Author/Creator:

Isaksen, Daniel C., 1972- author.

Series:

Memoirs of the American Mathematical Society ; no. 1269.

Memoirs of the American Mathematical Society, 0065-9266 ; number 1269

Language:

English

Subjects (All):

Homotopy theory.

Homotopy groups.

Algebraic topology.

Physical Description:

viii, 159 pages : illustrations ; 26 cm.

Place of Publication:

Providence : American Mathematical Society, [2019]

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.

Notes:

"November 2019; Volume 262; number 1269 (sixth of 7 numbers)."

Includes bibliographical references (page 151-153) and index.

ISBN:

9781470437886

1470437880

OCLC:

1121158657