The $ A_\infty$-structures and differentials of the Adams spectral sequence

DOI10.1070/IM2002V066N05ABEH000406zbMATH Open1080.55009arXivmath/0107006OpenAlexW3125257102MaRDI QIDQ4674567

V. A. Smirnov

Publication date: 17 May 2005

Published in: Izvestiya: Mathematics (Search for Journal in Brave)

Abstract: The Adams spectral sequence was invented by J.F.Adams 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 find inductive formulas for the differentials. It is based on the A_infty-structures, E_infty-structures and functional homology operations. As This approach it will be applied to the Kervaire invariant problem.

Full work available at URL: https://arxiv.org/abs/math/0107006

zbMATH Keywords

operadsAdams spectral sequence

Mathematics Subject Classification ID

Spectra with additional structure ((E_infty), (A_infty), ring spectra, etc.) (55P43) Adams spectral sequences (55T15) Loop space machines and operads in algebraic topology (55P48)

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