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Title:Computing the Goodwillie-Taylor tower of discrete modules
Author(s):Lior, Dan
Director of Research:McCarthy, Randy
Doctoral Committee Chair(s):Ando, Matthew
Doctoral Committee Member(s):McCarthy, Randy; Rezk, Charles; Nevins, Thomas A.
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):Goodwillie
Functor Calculus
Taylor Tower
Robinson Bicomplex
Discrete Module
Discrete Functor
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.
Issue Date:2013-02-03
URI:http://hdl.handle.net/2142/42374
Rights Information:Copyright 2012 Dan Lior
Date Available in IDEALS:2013-02-03
Date Deposited:2012-12


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