Reference request: Goodwillie tower of the identity

This is done by identifying the partition complex of the set with j elements with the space of fully grown trees with j+1 leaves. Reference: "Partition complexes, duality and integral tree representations" by Alan Robinson, Algebr. Geom. Topol. 4. See specifically proposition 2.7 and corollary 2.8. http://msp.org/agt/2004/4-2/agt-v4-n2-p12-s.pdf


Jean-Louis Loday told me about the extended action by $\Sigma_{j+1}$ in the fall of 1992, after an Oberwolfach talk I gave about the rank filtration of algebraic $K$-theory, where the $\Sigma_j$-representations given by the integral homology of the Goodwillie derivative spectra $W_j$ played a role. I had shown that these representations were freely generated by $j$-fold Lie brackets, and Loday knew the connection to spaces of trees. Maybe you were there, too?

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At.Algebraic Topology

Homotopy Theory

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