Stasheff structures and differentials of the Adams spectral sequence

2000/10/23 by V. A. Smirnov, Smirnov, V. A.
Mathematics · #Algebraic Topology (math.AT) #FOS: Mathematics #math.AT

paper · pdf · doi:10.48550/arxiv.math/0010214

31 pages

arxiv created 2000/10/23 · arxiv updated 2009/11/30

Abstract

The Adams spectral sequence was invented by J.F.Adams almost fifty years ago for calculations of stable homotopy groups of topological spaces and in particular of spheres. The calculation of differentials of this spectral sequence is one of the most difficult problem of Algebraic Topology. Here we consider an approach to solve this problem in the case of Z/2 coefficients and find inductive formulas for the differentials. It is based on the Stasheff algebra structures, operad methods and functional homology operations.

Related

• Automated differential computation in the Adams spectral sequence
• Computation of the E₃-term of the Adams spectral sequence
• The Adams differentials on the classes h_j³
• The E₃ page of the Adams spectral sequence
• Higher structure in the unstable Adams spectral sequence