Computing the Goodwillie-Taylor tower of discrete modules

Lior, Dan

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https://hdl.handle.net/2142/42374 Copy

Description

Title

Computing the Goodwillie-Taylor tower of discrete modules

Author(s)

Lior, Dan

Issue Date

2013-02-03T19:36:43Z

Director of Research (if dissertation) or Advisor (if thesis)

McCarthy, Randy

Doctoral Committee Chair(s)

Ando, Matthew

Committee Member(s)

• McCarthy, Randy
• Rezk, Charles
• Nevins, Thomas A.

Department of Study

Mathematics

Discipline

Mathematics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(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.

Graduation Semester

2012-12

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http://hdl.handle.net/2142/42374

Copyright and License Information

Copyright 2012 Dan Lior

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