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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
- Date of Ingest
- 2017-09-29T16:39:45Z
- 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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Graduate Dissertations and Theses at Illinois PRIMARY
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