61 citations · 438 across the 47 of their papers we have counts for
16 papers · 1 filter
Exotic cyclic cohomology classes and Lipschitz algebras
Magnus Goffeng, Ryszard Nest
We study the noncommutative geometry of algebras of Lipschitz continuous and Hölder continuous functions where non-classical and novel differential geometric invariants arise. Inde…
A higher Kac-Moody extension for two-dimensional gauge groups
Jens Kaad, Ryszard Nest, Jesse Wolfson
Let be a finite dimensional Lie group and consider the smooth double loop group, i.e. the Fréchet Lie group of smooth maps from the 2-torus to . For a finite dimensional Hil…
The orbit method for the Baum-Connes Conjecture for algebraic groups over local function fields
Siegfried Echterhoff, Kang Li, Ryszard Nest
The main purpose of this paper is to modify the orbit method for the Baum-Connes conjecture as developed by Chabert, Echterhoff and Nest in their proof of the Connes-Kasparov conje…
Equivariant Algebraic Index Theorem
Alexander Gorokhovsky, Niek de Kleijn, Ryszard Nest
We prove a Γ-equivariant version of the algebraic index theorem, where Γ is a discrete group of automorphisms of a formal deformation of a symplectic manifold. The particular cases…
The K-theory of twisted multipullback quantum odd spheres and complex projective spaces
Piotr M. Hajac, Ryszard Nest, David Pask +2
We find multipullback quantum odd-dimensional spheres equipped with natural -actions that yield the multipullback quantum complex projective spaces constructed from Toeplitz…
Tate tame symbol and the joint torsion of commuting operators
Jens Kaad, Ryszard Nest
We investigate determinants of Koszul complexes of holomorphic functions of a commuting tuple of bounded operators acting on a Hilbert space. Our main result shows that the analyti…
Canonical holomorphic sections of determinant line bundles
Jens Kaad, Ryszard Nest
We investigate the analytic properties of torsion isomorphisms (determinants) of mapping cone triangles of Fredholm complexes. Our main tool is a generalization to Fredholm complex…
A transformation rule for the index of commuting operators
Jens Kaad, Ryszard Nest
In the setting of several commuting operators on a Hilbert space one defines the notions of invertibility and Fredholmness in terms of the associated Koszul complex. The index prob…
Equivariant Poincaré duality for quantum group actions
Ryszard Nest, Christian Voigt
We extend the notion of Poincaré duality in KK-theory to the setting of quantum group actions. An important ingredient in our approach is the replacement of ordinary tensor product…
Fibrations with noncommutative fibers
Siegfried Echterhoff, Ryszard Nest, Herve Oyono-Oyono
We study an analogue of fibrations of topological spaces with the homotopy lifting property in the setting of C*-algebra bundles. We then derive an analogue of the Leray-Serre spec…
Principal noncommutative torus bundles
Siegfried Echterhoff, Ryszard Nest, Herve Oyono-Oyono
In this paper we study continuous bundles of C*-algebras which are non-commutative analogues of principal torus bundles. We show that all such bundles, although in general being ve…
C*-Algebras over Topological Spaces: The Bootstrap Class
Ralf Meyer, Ryszard Nest
We carefully define and study C*-algebras over topological spaces, possibly non-Hausdorff, and review some relevant results from point-set topology along the way. We explain the tr…
Chern character for twisted complexes
Paul Bressler, Alexander Gorokhovsky, Ryszard Nest +1
We construct a Chern character of a perfect complex of twisted modules over an algebroid stack.
Homological algebra in bivariant K-theory and other triangulated categories
Ralf Meyer, Ryszard Nest
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 set…
The Baum-Connes Conjecture via Localisation of Categories
Ralf Meyer, Ryszard Nest
We redefine the Baum-Connes assembly map using simplicial approximation in the equivariant Kasparov category. This new interpretation is ideal for studying functorial properties an…
Riemann-Roch via deformation quantization, II
Paul Bressler, Ryszard Nest, Boris Tsygan
We prove a Riemann-Roch formula for deformation quantization of complex manifolds and its corollary, an index theorem for elliptic pairs conjectured by Schapira and Schneiders.