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Abstract: We develop a functorial approach to the study of the homotopy groups ofspheres and Moore spaces $MA,n$, based on the Curtis spectral sequence andthe decomposition of Lie functors as iterates of simpler functors such as thesymmetric or exterior algebra functors. The discussion takes place over theintegers, and includes a functorial description of the derived functors ofcertain Lie algebra functors, as well as of all the main cubical functors suchas the degree 3 component $SP^3$ of the symmetric algebra functor. As anillustration of this method, we retrieve in a purely algebraic manner the3-torsion component of the homotopy groups of the 2-sphere up to degree 14, andgive a unified presentation of homotopy groups $\pi iMA,n$ for small valuesof both $n$ and $i$.



Author: Lawrence Breen, Roman Mikhailov

Source: https://arxiv.org/



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