Related papers: Deformation of finite dimensional C*-quantum group…

We show that the group ${\Cal D}(M)$ of pseudoisotopy classes of diffeomorphisms of a manifold of dimension $\geq 5$ and of finite fundamental group is commensurable to an arithmetic group. As a result $\pi_0(\text{{\it Diff\,M}})$ is a…

We give a survey of the theory of finite quantum groupoids (weak Hopf algebras), including foundations of the theory and applications to finite depth subfactors, dynamical deformations of quantum groups, and invariants of knots and…

We define a numerical quasi-isometry invariant of a finitely generated group, whose values parametrize the difference between the group being uniformly embeddable in a Hilbert space and the reduced C*-algebra of the group being exact.

Given a closed orientable Euclidean cone 3-manifold C with cone angles less than or equal to pi, and which is not almost product, we describe the space of constant curvature cone structures on C with cone angles less than pi. We establish a…

A finite quantum hypergroup is a finite-dimensional unital algebra $A$ over the field of complex numbers. There is a coproduct on $A$, a coassociative map from $A$ to $A\otimes A$ assumed to be unital, but it is not required to be an…

Given a normal subgroup bundle $\mathcal A$ of the isotropy bundle of a groupoid $\Sigma$, we obtain a twisted action of the quotient groupoid $\Sigma/\mathcal A$ on the bundle of group $C^*$-algebras determined by $\mathcal A$ whose…

We study the deformation complex of the dg wheeled properad of $\mathbb{Z}$-graded quadratic Poisson structures and prove that it is quasi-isomorphic to the even M. Kontsevich graph complex. As a first application we show that the…

Macbeath gave a formula for the number of fixed points for each non-identity element of a cyclic group of automorphisms of a compact Riemann surface in terms of the universal covering transformation group of the cyclic group. We observe…

We construct uncountably many mutually nonisomorphic simple separable stably finite unital exact C$^\ast$-algebras which are not isomorphic to their opposite algebras. In particular, we prove that there are uncountably many possibilities…

We consider the construction of twisted tensor products in the category of C*-algebras equipped with orthogonal filtrations and under certain assumptions on the form of the twist compute the corresponding quantum symmetry group, which turns…

Let $E$ be a Koszul Frobenius algebra. A Clifford deformation of $E$ is a finite dimensional $\mathbb Z_2$-graded algebra $E(\theta)$, which corresponds to a noncommutative quadric hypersurface $E^!/(z)$, for some central regular element…

We introduce a quantum automorphism group for hypergraphs, which turns out to generalize the quantum automorphism group of Bichon for classical graphs. Further, we show that our quantum automorphism group acts on hypergraph C*-algebras as…

We construct dense, unconditional subalgebras of the reduced group $C^*$-algebra of a word-hyperbolic group, which are closed under holomorphic functional calculus and possess many bounded traces. Applications to the cyclic cohomology of…

We give an alternative construction of the essential $C^*$-algebra of an \'etale groupoid, along with an ``amenability'' notion for such groupoids that is implied by the nuclearity of this essential $C^*$-algebra. In order to do this we…

We characterize the class of RFD $C^*$-algebras as those containing a dense subset of elements that attain their norm under a finite-dimensional representation. We show further that this subset is the whole space precisely when every…

In this article, we generalize to the case of measured quantum groupoids on a finite basis some important results concerning equivariant Kasparov theory for actions of locally compact quantum groups [S. Baaj and G. Skandalis, 1989, 1993].…

We study the geometry of infinitely presented groups satisfying the small cancelation condition C'(1/8), and define a standard decomposition (called the criss-cross decomposition) for the elements of such groups. We use it to prove the…

We prove that the groups of orientation-preserving homeomorphisms and diffeomorphisms of $\mathbb{R}^n$ are boundedly acyclic, in all regularities. This is the first full computation of the bounded cohomology of a transformation group that…

We investigate some coboundary map associated to a $3$-dimensional terminal singularity which is important in the study of deformations of singular $3$-folds. We prove that this map vanishes only for quotient singularities and a…

We prove that any compact surface with constant positive curvature and conical singularities can be decomposed into irreducible components of standard shape, glued along geodesic arcs connecting conical singularities. This is a spherical…