Algebraic K-theory and abstract homotopy theory
AJ Blumberg, MA Mandell - Advances in Mathematics, 2011 - Elsevier
We decompose the K-theory space of a Waldhausen category in terms of its Dwyer–Kan
simplicial localization. This leads to a criterion for functors to induce equivalences of K …
simplicial localization. This leads to a criterion for functors to induce equivalences of K …
Derived Koszul duality and involutions in the algebraic K‐theory of spaces
AJ Blumberg, MA Mandell - Journal of Topology, 2011 - Wiley Online Library
We interpret different constructions of the algebraic K‐theory of spaces as an instance of
derived Koszul (or bar) duality and also as an instance of Morita equivalence. We relate the …
derived Koszul (or bar) duality and also as an instance of Morita equivalence. We relate the …
Localization for THH (ku) and the topological Hochschild and cyclic homology of Waldhausen categories
AJ Blumberg, MA Mandell - arXiv preprint arXiv:1111.4003, 2011 - arxiv.org
We prove a conjecture of Hesselholt and Ausoni-Rognes, establishing localization cofiber
sequences of spectra for THH (ku) and TC (ku). These sequences support Hesselholt's view …
sequences of spectra for THH (ku) and TC (ku). These sequences support Hesselholt's view …