It is proved that classifiable simple separable nuclear purely infinite C∗algebras having finitely generated K-theory and torsion-free K1 are semiprojective. This is accomplished by exhibiting these algebras as C∗-algebras of infinite directed graphs.

We establish that, given Σ a compact orientable surface, and G a finitely presented one-ended group, the set of copies of G in the mapping class group MCG(Σ) consisting of only pseudo-Anosov elements except identity, is finite up to conjugacy. This relies on a result of Bowditch on the same problem for images of surfaces groups. He asked us whether we could reduce the case of one-ended groups t...

Computably enumerable algebras are the ones whose positive atomic diagrams are computably enumerable. Computable algebras are the ones whose atomic diagrams are computable. In this paper we investigate computably enumerable algebras and provide several algebraic and computable theoretic distinctions of these algebras from the class of computable algebras. We give a characterization of computabl...

We rigorously define the Liouville action functional for the finitely generated, purely loxodromic quasi-Fuchsian group using homology and cohomology double complexes naturally associated with the group action. We prove that classical action – the critical value of the Liouville action functional, considered as a function on the quasiFuchsian deformation space, is an antiderivative of a 1-form ...

It is well known [4, p. 265; 3] that the space 7,i[0, l] is not isomorphic with a conjugate space. At the other extreme, it is also well known that h is isometric with the conjugate space of Co. Each of these is an example of a space of all real-valued integrable functions over a measure space (T, p), a major difference between them being that the measure space underlying 7_i[0, l] has no atoms...

Let A be a finitely generated commutative algebra over a field K with a presentation A = K〈X1, . . . , Xn | R〉, where R is a set of monomial relations in the generators X1, . . . , Xn. So A = K[S], the semigroup algebra of the monoid S = 〈X1, . . . , Xn | R〉. We characterize, purely in terms of the defining relations, when A is an integrally closed domain, provided R contains at most two relati...

We prove that finitely generated purely loxodromic subgroups of a right-angled Artin group A(Γ) fulfill equivalent conditions that parallel characterizations of convex cocompactness in mapping class groups Mod(S). In particular, such subgroups are quasiconvex in A(Γ). In addition, we identify a milder condition for a finitely generated subgroup of A(Γ) that guarantees it is free, undistorted, a...

Effectiveness issues in algebra and model theory have been investigated intensively in the last thirty years. One wishes to understand the effective content of model-theoretic and algebraic results, and the interplay between notions of computability, algebra, and model theory. A significant body of work has recently been done in the area, and this is attested by recent series of Handbooks and s...