Localization for $THH(ku)$ and the Topological Hochschild and Cyclic Homology of Waldhausen Categories (Memoirs of the American Mathematical Society)

About the Author Andrew J. Blumberg, The University of Texas, Austin, TX, USA.Michael A. Mandell, Indiana University, Bloomington, IN, USA. Product Description The authors develop a theory of $THH$ and $TC$ of Waldhausen categories and prove the analogues of Waldhausen's theorems for $K$-theory. They resolve the longstanding confusion about localization sequences in $THH$ and $TC$, and establish a specialized devissage theorem. As applications, the authors prove conjectures of Hesselholt and Ausoni-Rognes about localization cofiber sequences surrounding $THH(ku)$, and more generally establish a framework for advancing the Rognes program for studying Waldhausen's chromatic filtration on $A(*)$.