Computing the Goodwillie-Taylor tower of discrete modules
Let $P_m$ and $D_m$ be the $m^{th}$ level and layer of the Goodwillie-Taylor tower for discrete modules. In \cite{intermont_johnson_mccarthy08} the rank filtration of $D_1F$ is described and the associated spectral sequence is shown to be equivalent to the filtration by rows of the reduced Robinson bicomplex of $F$. We consider the rank filtrations of $P_mF$ and $D_mF$ and give explicit descriptions of the entries of the $E^1$ page of the associated spectral sequences. In the case $m=1$ these entries agree with those of the spectral sequence associated with the reduced Robinson bicomplex.
Goodwillie, Functor Calculus, Taylor Tower, Robinson Bicomplex, Discrete Module, Discrete Functor
University of Illinois - Urbana-Champaign
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University of Illinois at Urbana-Champaign