The Goodwillie tower of free augmented algebras over connective ring spectra
| dc.contributor.advisor | Blumberg, Andrew J. | |
| dc.creator | Pancia, Matthew | en |
| dc.date.accessioned | 2015-02-10T21:27:10Z | en |
| dc.date.issued | 2014-12 | en |
| dc.date.submitted | December 2014 | en |
| dc.date.updated | 2015-02-10T21:27:10Z | en |
| dc.description | text | en |
| dc.description.abstract | Let R be a connective ring spectrum and let M be an R-bimodule. In this paper we prove several results that relate the K-theory of R⋉M and T[superscript M, subscript R] to a “topological Witt vectors” construction W(R; M), where R ⋉ M is the square-zero extension of R by M and T [superscript M, subscript R] is the tensor algebra on M. Our main results include a desciption of the Taylor tower of K(R ⋉ (−)) and the derived functor of K̃(TR(−)) on the category of R-bimodules in terms of the Taylor tower of W(R;−). W(R;−) has an easily described Taylor tower, given explicitly by Lindenstrauss and McCarthy in [17]. Our main results serve as generalizations of the results for discrete rings in [17, 18] and also extend the computations by Hesselholt and Madsen [15] showing that π₀(TR(R; p)) is isomorphic to the p-typical Witt vectors over R when R a commutative ring. | en |
| dc.description.department | Mathematics | en |
| dc.format.mimetype | application/pdf | en |
| dc.identifier.uri | http://hdl.handle.net/2152/28423 | en |
| dc.language.iso | en | en |
| dc.subject | K-theory | en |
| dc.subject | Algebraic topology | en |
| dc.subject | Witt vectors | en |
| dc.title | The Goodwillie tower of free augmented algebras over connective ring spectra | en |
| dc.type | Thesis | en |
| thesis.degree.department | Mathematics | en |
| thesis.degree.discipline | Mathematics | en |
| thesis.degree.grantor | The University of Texas at Austin | en |
| thesis.degree.level | Doctoral | en |
| thesis.degree.name | Doctor of Philosophy | en |