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After investigating by examples the unusual and striking elementary properties of the Penrose tilings and the Arnold cat map, we associate a finite symbolic dynamics with finite grammar rules to each of them. Instead of studying these…

In previous definition of $\mathrm{E}$-theory, separability of the $\mathrm{C}^*$-algebras is needed either to construct the composition product or to prove the long exact sequences. Considering the latter, the potential failure of the long…

We study the structure and compute the stable rank of C*-algebras of finite higher-rank graphs. We completely determine the stable rank of the C*-algebra when the k-graph either contains no cycle with an entrance, or is cofinal. We also…

Given a locally convex space $(\mathcal{A},\tau)$ with a Hausdorff locally convex topology $\tau$ such that the following maps are continuous; $u \mapsto u^*$ for all $u \in \mathcal{A}$, $x \mapsto x\cdot y$ and $x \mapsto z\cdot x$ for…

We study connected components of the Morse boundary and their stabilisers. We introduce the notion of point-convergence and show that if the set of non-singleton connected components of the Morse boundary of a finitely generated group $G$…

We show that every topological k-graph constructed from a locally compact Hausdorff space {\Omega} and a family of pairwise commuting local homeomorphisms on {\Omega} satisfying a uniform boundedness condition on the cardinalities of…

We consider Hilsum's notion of bordism as an equivalence relation on unbounded $KK$-cycles and study the equivalence classes. Upon fixing two $C^*$-algebras, and a $*$-subalgebra dense in the first $C^*$-algebra, a…

We establish isomorphism ranges for the comparison maps between algebraic and topological K-groups, extending classical Quillen-Lichtenbaum conjecture to separated complex schemes of finite type after refinement. Additionally, we…

We show that coarse maps between countable metric spaces of bounded geometry induce natural transformations of sufficiently good endofunctors of C*-algebras and prove that this correspondence is invariant with respect to coarse homotopies.

The completion of a (normed) $C^*$-algebra $A_0[\| \cdot \|_0]$ with respect to a locally convex topology $\tau$ on $A_0$ that makes the multiplication of $A_0$ separately continuous is, in general, a quasi *-algebra, and not a locally…

We prove that the coarse assembly maps for proper metric spaces which are non-positively curved in the sense of Busemann are isomorphisms, where we do not assume that the spaces are with bounded coarse geometry. Also it is shown that we can…

Convolution semigroups of states on a quantum group form the natural noncommutative analogue of convolution semigroups of probability measures on a locally compact group. Here we initiate a theory of weakly continuous convolution semigroups…

We consider classes of diffeomorphisms of Euclidean space with partial asymptotic expansions at infinity; the remainder term lies in a weighted Sobolev space whose properties at infinity fit with the desired application. We show that two…

Let $\A$ and $\B$ be operator algebras with $c_0$-isomorphic diagonals and let $\K$ denote the compact operators. We show that if $\A\otimes\K$ and $\B\otimes\K$ are isometrically isomorphic, then $\A$ and $\B$ are isometrically isomorphic.…

We study the topological dynamics by iterations of a piecewise continuous, non linear and locally contractive map in a real finite dimensional compact ball. We consider those maps satisfying the "separation property": different continuity…

We show that semigroup C*-algebras attached to ax+b-semigroups over rings of integers determine number fields up to arithmetic equivalence, under the assumption that the number fields have the same number of roots of unity. For finite…

We show that a $KK$-equivalence between two unital $C^*$-algebras produces a correspondence between their DG categories of finitely generated projective modules which is a $\mathbf{K}_*$-equivalence, where $\mathbf{K}_*$ is Waldhausen's…

K-Theory for hermitian symmetric spaces of non-compact type, as developed recently by the authors, allows to put Cartan's classification into a homological perspective. We apply this method to the case of inductive limits of finite…

A surjective endomorphism or, more generally, a polymorphism in the sense of \cite{SV}, of a compact abelian group $H$ induces a transformation of $L^2(H)$. We study the C*-algebra generated by this operator together with the algebra of…

The bounded localization $\beta_b$ of a locally convex topology $\beta$ is defined as the finest locally convex topology agreeing with $\beta$ on all bounded sets. We show that the strict topology on the multiplier algebra of a bornological…