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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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