Cyclic homology was introduced in the early eighties independently by Connes and Tsygan.
They came from different directions. Connes wanted to associate homological invariants to K …

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 …

In his foundational paper on cyclic cohomology [Co], A. Connes introduced, besides the
ordinary cyclic cohomology, also the periodic theory. This was motivated, in the first place …

In this work we study the failure of the HKR theorem over rings of positive and mixed
characteristic. For this we construct a filtered circle interpolating between the usual …

We introduce Γ-homology, the natural homology theory for E∞-algebras, and a cyclic
version of it. Γ-homology specializes to a new homology theory for discrete commutative …

In 1985 B6kstedt [2] introduced the topological Hochschild homology functor THH which is
related to Waldhausen's algebraic K-theory of certain A~ rings [26] in a way similar to the …

Since their introduction 20 years ago, the evaluation of Quillen's higher algebraic K—groups
of rings [35] has remained a difl-icult problem in homo-topy theory. One does have Quillen's …

We study the homology of SLn (F [t, t− 1]) by examining the action of the group on a suitable
simplicial complex. The E1-term of the resulting spectral sequence is computed and the …

This paper calculates the relative algebraic K-theory K∗(k [x]/(xn),(x)) of a truncated
polynomial algebra over a perfect field k of positive characteristic p. Since the ideal …

Using the formalism of Grothendieck's derivators, we construct the universal localizing
invariant of differential graded (dg) categories. By this we mean a morphism U l from the …