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Showing 1 to 15 of 15 for “"Goodwillie"”.
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Goodwillie Calculi
"We define an ""algebraic"" version of the Goodwillie tower, Pdn F(X), that depends only on the behaviour of F on coproducts of X. When F is a functor to connected spaces or grouplike H-spaces, the functor Pdn F is the base of a fibration &vbm0;⊥*+1F&vbm0;→ F→P dnF, whose fiber is …
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Goodwillie calculus and I
… category of finite sets and injective maps in Goodwillie's calculus of homotopy functors. By careful analysis of the cross-effects of a reduced endofunctor of based spaces, this point of view leads to a monoidal model for the derivatives. Such structure induces operad and module structures for …
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Motivic Polylogarithms for the Goodwillie -Lichtenbaum Complex
We also construct a homomorphism from H1M (Spec C,Z (n)) to R using differential forms and prove that it generalizes D. We expect it agree with the Borel regulator map up to a constant multiplication.
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Computing the Goodwillie-Taylor tower of discrete modules
… and $D_m$ be the $m^{th}$ level and layer of the Goodwillie-Taylor tower for discrete modules. In \cite{intermont_johnson_mccarthy08} the rank filtration of $D_1F$ is described and the associated spectral sequence is shown to be equivalent to the filtration by rows of the reduced Robinson …
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Computing the Goodwillie-Taylor tower for discrete modules
… 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. …
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Goodwillie calculus and algebras over a spectral operad
… goal of this thesis is to apply the theory of Goodwillie calculus to the category Algo of algebras over a spectral operad. Its first part generalizes many of the original results of Goodwillie in [14] so that they apply to a larger class of model categories and hence be applicable to Algo. The …
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Bar constructions for topological operads and the Goodwillie derivatives of the identity
… structure on the partition poset models for the Goodwillie derivatives of the identity functor on based spaces and show that this induces the 'lie' operad structure on the homology groups of these derivatives. Finally, we extend the bar construction to modules over operads (and, dually, to …
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On Hopf Algebra Type and Rational Calculus Decompositions
… which is joint work with Randy McCarthy, uses Goodwillie calculus to extend this result to a much larger class of functors. A Hopf algebra A is both an algebra with a multiplication map m:A⊗A→ A and a coalgebra with a comultiplication map D: A→A⊗A which must behave well …
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Unstable chromatic homotopy theory
… of the telescope conjecture. I make use the Goodwillie tower of the identity functor, which resolves the unstable spheres into spectra which are the Steinberg summands of classifying spaces of the additive groups of vector spaces over F,. By understanding the attaching maps of the Goodwillie …
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Cosimplicial invariants and Calculus of homotopy functors
… and the other by Waldhausen (using a variant of Goodwillie’s Taylor tower). The proof of agreement of these constructions relies heavily on the fact that the functors involved take values in Spectra. Goodwillie conjectured the extension of these results to include the case of functors taking …
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Automorphisms and symbols in K(,2)
… groups of topology. In this work we consider Goodwillie and Lichtenbaum's candidate for motivic cohomology. For R a regular ring, they define a ""weight"" filtration on the K-theory space K(R),$$K(R) = W\sp0 \gets W\sp1 \gets W\sp2 \gets \cdots,$$and then define the cohomology groups to …
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The algebraic K-theory of the chromatic filtration and the telescope conjecture
… pi₀. Using this and an extension of the Dundas--Goodwillie--McCarthy theorem to —1-connective ring spectra, we obtain a formula for the algebraic K-theory of the K(1)-local sphere in terms of topological cyclic homology of a ring spectrum j_zeta, and in particular find that its algebraic K-groups …
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Coloring and constructing (hyper)graphs with restrictions
… poset. A lower bound of sqrt(dn) was observed by Goodwillie. We provide a sublinear upper bound.
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Stabilizing spectral functors of exact categories
This Dissertation was approved for publication on 2017-07-13 at 15:08.