Growth of homotopy groups of spheres via the Goodwillie-EHP Sequence

2022/01/20 by Boyde, Guy
#55Q40 (Primary) 18F50 (Secondary) #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2201.08100

Abstract

We bound the volume of the homotopy groups of the 2-local Goodwillie approximations of a sphere in terms of the amount of 2-torsion in the stable stems, providing a Goodwillie-theoretic refinement of a result of Burklund and Senger (arXiv:2203.00670). At the 2^k-excisive approximation, this bound is obtained by `multiplying the stable answer by a polynomial of degree k'. The main tool is Behrens' Goodwillie-EHP Long Exact Sequence.

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