Topological cyclic homology is a manifestation of Waldhausen's vision that the cyclic theory
of Connes and Tsygan should be developed with the initial ring S of higher algebra as base …

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 …

We give a survey of cyclic homology/cohomology theory including a detailed discussion of
cyclic theories for various classes of topological algebras. We show how to associate cyclic …

We investigate higher topological cyclic homology as an approach to studying chromatic
phenomena in homotopy theory. Higher topological cyclic homology is constructed from the …

This paper reviews the relations between algebraic K-theory and topological cyclic
homology given by cyclotomic trace. If one, very superficially, views algebraic K-theory as …

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 …

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 …

1.1. Topological cyclic homology is the codomain of the cyclotomic trace from algebraic i^-
theory trc: K (L)-> TC (L). It was defined in [2] but for our purpose the exposition in [6] is more …

Given a henselian pair $(R, I) $ of commutative rings, we show that the relative $ K $-theory
and relative topological cyclic homology with finite coefficients are identified via the …

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