Computing the Goodwillie-Taylor tower for discrete modules

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2017

Author dc:creator

• Tebbe, Amelia Nora

Contributors dc:contributor

• McCarthy, Randy
• Ando, Matt
• Rezk, Charles
• Malkiewich, Cary

• Functor calculus
• Goodwillie calculus
• Discrete modules
• Atomic functors
• Finite sets
• Rank filtration
• Algebraic topology
• Homotopy theory

Statement dc:rights

• Copyright 2017 Amelia Tebbe

Language dc:language

en

Handle dc:identifier

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

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/98276