Bivariant (equivariant) K-theory is the standard setting for non-commutative topology. We
may carry over various techniques from homotopy theory and homological algebra to this …

Topological K-theory of complex noncommutative spaces Page 1 Topological K-theory of
complex noncommutative spaces Anthony Blanc Compositio Math. 152 (2016), 489–555 …

Making use of the theory of noncommutative motives, we characterize the topological
Dennis trace map as the unique multiplicative natural transformation from algebraic K-theory …

Non-commutative topology deals with topological properties of C*-algebras. Already in the
1970s, the classification of AF-algebras by K-theoretic data [15] and the work of Brown …

We use homological ideals in triangulated categories to get a sufficient criterion for a pair of
subcategories in a triangulated category to be complementary. We apply this criterion to …

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 …

In this article we continue the development of a theory of noncommutative motives, initiated
in [30]. We construct categories of A1-homotopy noncommutative motives, describe their …

We show that the K–theory construction of our paper [Adv. Math 205 (2006) 163-228], which
preserves multiplicative structure, extends to a symmetric monoidal closed bicomplete …

We prove that the cyclic homology of a saturated A_ ∞ A∞ category admits the structure of a
'polarized variation of Hodge structures', building heavily on the work of many authors: the …

For a recollement of derived module categories of rings, we provide sufficient conditions to
guarantee the additivity formula of higher algebraic K-groups of the rings involved, and …