University of Illinois Urbana-Champaign

Computing the Goodwillie-Taylor tower for discrete modules

Tebbe, Amelia Nora

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https://hdl.handle.net/2142/98276

Description

Title
Computing the Goodwillie-Taylor tower for discrete modules
Author(s)
Tebbe, Amelia Nora
Issue Date
2017-07-11
Director of Research (if dissertation) or Advisor (if thesis)
McCarthy, Randy
Doctoral Committee Chair(s)
Ando, Matt
Committee Member(s)
  • Rezk, Charles
  • Malkiewich, Cary
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
  • Functor calculus
  • Goodwillie calculus
  • Discrete modules
  • Atomic functors
  • Finite sets
  • Rank filtration
  • Algebraic topology
  • Homotopy theory
Abstract
A functor from finite sets to chain complexes is called atomic if it is completely determined by its value on a particular set. We present a new resolution for these atomic functors, which allows us to easily compute their Goodwillie polynomial approximations. By a rank filtration, any functor from finite sets to chain complexes is built from atomic functors. Computing the linear approximation of an atomic functor is a classic result involving partition complexes. Robinson constructed a bicomplex, which can be used to compute the linear approximation of any functor. We hope to use our new resolution to similarly construct bicomplexes that allow us to compute polynomial approximations for any functor from finite sets to chain complexes.
Graduation Semester
2017-08
Type of Resource
text
Permalink
http://hdl.handle.net/2142/98276
Copyright and License Information
Copyright 2017 Amelia Tebbe

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