Topological cyclic homology is a refinement of Connes–Tsygan's cyclic homology which
was introduced by Bökstedt–Hsiang–Madsen in 1993 as an approximation to algebraic K …

Let f: A-~ B be a map of rings up to homotopy (or" FSP's", see eg [B61],[B53] or Definition 3.1
below). When is it possible to give a good description of the relative algebraic K-theory …

Let A be an A∞ ring spectrum. We use the description from our preprint [math. AT/0612165]
of the cyclic bar and cobar construction to give a direct definition of topological Hochschild …

Algebraic K-theory encodes important invariants for several mathematical disciplines,
spanning from geometric topology and functional analysis to number theory and algebraic …

The cyclotomic trace is a map from algebraic K-theory of a group ring to a certain topological
refinement of cyclic homology. The target is naturally mapped to topological Hochschild …

We construct localization cofibration sequences for the topological Hochschild homology
(THH) and topological cyclic homology (TC) of small spectral categories. Using a global …

A functor is defined which detects stable equivalences of symmetric spectra. As an
application, the definition of topological Hochschild homology on symmetric ring spectra …

Algebraic K-Theory plays an important role in many areas of modern mathematics: most
notably algebraic topology, number theory, and algebraic geometry, but even including …

In recent years, the study of the algebraic K-theory space K (R) of a ring R has been
approached by the introduction of spaces with a more homological flavor. One collection of …

From the reviews:" This is a very interesting book containing material for a comprehensive
study of the cyclid homological theory of algebras, cyclic sets and S1-spaces. Lie algebras …