Computing the Goodwillie-Taylor tower of discrete modules
type: CreativeWork
description: 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.
abstract: 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.
author: Lior, Dan
language: en
keywords: Goodwillie, Functor Calculus, Taylor Tower, Robinson Bicomplex, Discrete Module, Discrete Functor
date published: 2013-02-03T19:36:43Z
date modified: 2026-07-22T22:25:33Z
provider: University of Illinois - Urbana-Champaign
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: University of Illinois at Urbana-Champaign

PropertyValue
property ID: Handle
value: http://hdl.handle.net/2142/42374