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 …

arXiv:math/0402405v1 [math.KT] 25 Feb 2004 Page 1 arXiv:math/0402405v1 [math.KT] 25
Feb 2004 The Baum-Connes and the Farrell-Jones Conjectures in K- and L-Theory Wolfgang …

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 …

We prove a purity property in telescopically localized algebraic $ K $-theory of ring spectra:
For $ n\geq 1$, the $ T (n) $-localization of $ K (R) $ only depends on the $ T …

We present the status of the Farrell–Jones Conjecture for algebraic K-theory for a group G
and arbitrary coefficient rings R. We add new groups for which the conjecture is known to be …

Cut-and-paste-theory has recently emerged as an important variant of higher algebraic-
theory. However, many of the powerful tools used to study classical higher algebraic-theory …

Manifolds are the central geometric objects in modern mathematics. An attempt to
understand the nature of manifolds leads to many interesting questions. One of the most …

Motivated by the Farrell-Jones Conjecture for group rings, we formulate the $\mathcal {C} $
op-Farrell-Jones Conjecture for the K-theory of Hecke algebras of td-groups. We prove this …

The chapter explains quickest and probably for a homotopy theorist most convenient
approach to assembly maps is via homotopy colimits. The Farrell-Jones Conjecture and the …

This manuscript is not finished. Most of it is in nearly final form, whereas Chapters 8 and 25
are still under construction. Comments are very welcome. The Isomorphism Conjectures due …