Related papers: Unbounded symmetric operators in $K$-homology and …

This paper studies the K-homology of a crossed product of a discrete group acting smoothly on a manifold, with a better understanding of the noncommutative geometry of the crossed-product as the primary goal, and the Baum-Connes apparatus…

We compute the equivariant $K$-homology of the classifying space for proper actions, for compact 3-dimensional hyperbolic reflection groups. This coincides with the topological $K$-theory of the reduced $C^\ast$-algebra associated to the…

We extend the notion of a spectral triple to that of a higher-order relative spectral triple, which accommodates several types of hypoelliptic differential operators on manifolds with boundary. The bounded transform of a higher-order…

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 construct the Baum-Connes assembly map for locally…

We reveal a correspondence between the homological torsion of the Bianchi groups and new geometric invariants, which are effectively computable thanks to their action on hyperbolic space. We use it to explicitly compute their integral group…

In this paper, we introduce a property of topological dynamical systems that we call finite dynamical complexity. For systems with this property, one can in principle compute the $K$-theory of the associated crossed product $C^*$-algebra by…

Given an ample groupoid, we construct a spectral sequence with groupoid homology with integer coefficients on the second sheet, converging to the K-groups of the (reduced) groupoid C*-algebra, provided the groupoid has torsion-free…

We associate a non-commutative $C^*$-algebra with any locally finite simplicial complex. We determine the $K$-theory of these algebras and show that they can be used to obtain a conceptual explanation for the Baum-Connes conjecture.

We prove the $K$-theoretic Farrell-Jones conjecture for groups as in the title with coefficient rings and $C^*$-algebras which are stable with respect to compact operators. We use this and Higson-Kasparov's result that the Baum-Connes…

Noncommutative K\"ahler structures were recently introduced as an algebraic framework for studying noncommutative complex geometry on quantum homogeneous spaces. In this paper, we introduce the notion of a \emph{compact quantum homogeneous…

Given a manifold with corners $X$, we associates to it the corner structure simplicial complex $\Sigma_X$. Its reduced K-homology is isomorphic to the K-theory of the $C^*$-algebra $\mathcal{K}_b(X)$ of b-compact operators on $X$. Moreover,…

We develop an algebraic formalism for topological $\mathbb{T}$-duality. More precisely, we show that topological $\mathbb{T}$-duality actually induces an isomorphism between noncommutative motives that in turn implements the well-known…

We prove index formulas for elliptic operators acting between sections of C*-vector bundles on a closed manifold. The formulas involve Karoubi's Chern character from K-theory of a C*-algebra to de Rham homology of smooth subalgebras. We…

The Dirac-Dolbeault operator for a compact K\"ahler manifold is a special case of a Dirac operator. The Green function for the Dirac Laplacian over a Riemannian manifold with boundary allows to express the values of the sections of the…

We study boundary conditions for elliptic operators on non-compact manifolds with boundary via uniform K-homology, a version of K-homology sensitive to the large-scale geometry of the manifold. To that end, we develop the theory of relative…

By a result of Nagy, the C*-algebra of continuous functions on the q-deformation G_q of a simply connected semisimple compact Lie group G is KK-equivalent to C(G). We show that under this equivalence the K-homology class of the Dirac…

We prove in this paper that the periodic cyclic homology of the quantized algebras of functions on coadjoint orbits of connected and simply connected Lie group, are isomorphic to the periodic cyclic homology of the quantized algebras of…

We give a formulation of a deformation of Dirac operator along orbits of a group action on a possibly non-compact manifold to get an equivariant index and a K-homology cycle representing the index. We apply this framework to non-compact…

Let $F$ be a finite group. We consider the lamplighter group $L=F\wr\mathbb{Z}$ over $F$. We prove that $L$ has a classifying space for proper actions $\underline{E} L$ which is a complex of dimension two. We use this to give an explicit…

We give a new proof of the absence of non-trivial idempotents in the group ring of torsion-free cocompact lattices in SL(n,C). It is based on the following procedure. We lift the class of the trace in the cyclic cohomology of the group ring…