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Title:Computing the Goodwillie-Taylor tower for discrete modules
Author(s):Tebbe, Amelia Nora
Director of Research:McCarthy, Randy
Doctoral Committee Chair(s):Ando, Matt
Doctoral Committee Member(s):Rezk, Charles; Malkiewich, Cary
Department / Program:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Subject(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.
Issue Date:2017-07-11
Rights Information:Copyright 2017 Amelia Tebbe
Date Available in IDEALS:2017-09-29
Date Deposited:2017-08

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