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Title:Stabilizing spectral functors of exact categories
Author(s):Villeta-Garcia, Juan S
Director of Research:McCarthy, Randy
Doctoral Committee Chair(s):Ando, Matthew
Doctoral Committee Member(s):Rezk, Charles; Malkiewich, Cary
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):Algebraic K-Theory
Goodwillie Calculus
Homotopy Theory
Algebraic Topology
Abstract:We define and study the $K$-theory of exact categories with coefficients in endofunctors of spectra in analogy with Mitchell's homology of categories. Generalizing computations of McCarthy, we determine, for a discrete ring $R$, the $K$-theory of the exact category of finitely-generated projective $R$-modules with coefficients in the $n$-fold smash product functor. This computation allows us to analyze the effects of applying this functorial construction to the Goodwillie Taylor tower of a homotopy endofunctor of spectra. In the case of $\Sigma^\infty\Omega^\infty$, the associated tower recovers the Taylor tower of relative $K$-theory as computed by Lindenstrauss and McCarthy.
Issue Date:2017-07-13
Type:Thesis
URI:http://hdl.handle.net/2142/98290
Rights Information:Copyright 2017 Juan Villeta-Garcia
Date Available in IDEALS:2017-09-29
Date Deposited:2017-08


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