The Convergences of Part of Algebraic Representatives

Abstract

Both Adams spectral sequence and Adams–Novikov spectral sequence converge to the stable homotopy groups of sphere π_*(S). Suppose an element x in the E₂-term of the Adams–Novikov spectral sequence converges to a homotopy element in π_*(S). In this paper we determine that the algebraic representative \tilde{x} in the E₂-term of the Adams spectral sequence converges to the same homotopy element under the conditions related to the Novikov weight and homological dimension.

Keywords

Adams spectral sequence / Adams resolution / geometric boundary theorem / algebraic representative

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Peking University 2024