Cosimplicial invariants and Calculus of homotopy functors

The origin of these investigations was the successful attempt by myself and coauthors to generalize rational equivalences of two constructions which suggest possible definitions of deRham cohomology of “brave new” rings, one of Rezk (using a cosimplicial resolution) 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 value in Spaces. The main result of my thesis is a proof of this conjecture (Theorem 7.1.2), using significantly different methods than in the stable setting of the joint work. This makes strong use of the intermediate constructions T_n F in Goodwillie’s Calculus of homotopy functors. I give a new model which naturally gives rise to a new family of towers filtering the Taylor Tower of a functor. I also establish a surprising equivalence between the homotopy inverse limits of these towers and the homotopy inverse limits of certain cosimplicial resolutions. This equivalence gives a greatly simplified construction for the homotopy inverse limit of the Taylor tower of a functor F under general assumptions.

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

2012

Author dc:creator

• Eldred, Rosona

Contributors dc:contributor

• McCarthy, Randy
• Rezk, Charles
• Guillou, Bertrand

• Goodwillie Calculus
• Homotopy Theory
• Algebraic Topology
• homotopy functor
• homotopy limit

Statement dc:rights

• Copyright 2011 Rosona Eldred

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/29665

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/29665