Related papers: L^2-Betti numbers arising from the lamplighter gro…

In this paper, we show how to construct examples of closed manifolds with explicitly computed irrational, even transcendental L2 Betti numbers, defined via the universal covering. We show that every non-negative real number shows up as an…

We reconsider work of Elkalla on subnormal subgroups of 3-manifold groups, giving essentially algebraic arguments that extend to the case of $PD_3$-groups and group pairs. However the argument relies on an $L^2$-Betti number hypothesis…

We show that the Novikov-Shubin invariant of an element of the integral group ring of the lamplighter group Z_2 \wr Z can be irrational. This disproves a conjecture of Lott and Lueck. Furthermore we show that every positive real number is…

The main result is a general approximation theorem for normalised Betti numbers for Farber sequences of lattices in totally disconnected groups. Further, we contribute some computations and complements to the general theory of $L^2$-Betti…

We compute $L^2$-Betti numbers of postliminal, locally compact, unimodular groups in terms of ordinary dimensions of reduced cohomology with coefficients in irreducible unitary representations and the Plancherel measure. This allows us to…

We calculate all $\ell^2$-Betti numbers of the universal discrete Kac quantum groups $\hat U_n^+$ as well as their full half-liberated counterparts $\hat U_n^*$.

In this paper, we introduce a new technique in the study of the $*$-regular closure of some specific group algebras $KG$ inside $\mathcal{U}(G)$, the $*$-algebra of unbounded operators affiliated to the group von Neumann algebra…

We construct a family of simple, lacunary hyperbolic groups with property $(T)$ that have rational cohomological dimension~$16$ and whose second $\ell^2$-Betti number can be prescribed to be any positive real. Moreover, we construct…

Let $G$ be a countable group and $k$ a positive integer, we show that the $L^2$-Betti numbers of the group $G$ vanish up to degree $k$ provided that there is some infinite index subgroup $H$ with finite $k$th $L^2$-Betti number containing a…

We show that there exist non-unitarizable groups without non-abelian free subgroups. Both torsion and torsion free examples are constructed. As a by-product, we show that there exist finitely generated torsion groups with non-vanishing…

We show that the first $L^2$-betti number of a finitely generated residually finite group can be estimated from below by using ordinary first betti numbers of finite index normal subgroups. As an application we construct a finitely…

This article presents a method for proving upper bounds for the first $\ell^2$-Betti number of groups using only the geometry of the Cayley graph. As an application we prove that Burnside groups of large prime exponent have vanishing first…

We compute the $L^2$-Betti numbers of the free $C^*$-tensor categories, which are the representation categories of the universal unitary quantum groups $A_u(F)$. We show that the $L^2$-Betti numbers of the dual of a compact quantum group…

We determine the L^2-Betti numbers of all one-relator groups and all surface-plus-one-relation groups (surface-plus-one-relation groups were introduced by Hempel who called them one-relator surface groups). In particular we show that for…

We present a new method to construct finitely generated, residually finite, infinite torsion groups. In contrast to known constructions, a profinite perspective enables us to control finite quotients and normal subgroups of these torsion…

We introduce a notion of $L^2$-Betti numbers for locally compact, second countable, unimodular groups. We study the relation to the standard notion of $L^2$-Betti numbers of countable discrete groups for lattices. In this way, several new…

In this note we explain how the computation of the spectrum of the lamplighter group from \cite{Grigorchuk-Zuk(2000)} yields a counterexample to a strong version of the Atiyah conjectures about the range of $L^2$-Betti numbers of closed…

We generalise results of Thomas, Allcock, Thom-Petersen, and Kar-Niblo to the first $\ell^2$-Betti number of quotients of certain groups acting on trees by subgroups with free actions on the edge sets of the graphs.

We prove a Kunneth formula computing the Connes-Shlyakhtenko L^2-Betti numbers of the algebraic tensor product of two tracial *-algebras in terms of the L^2-Betti numbers of the two original algebras. As an application, we construct…

We study the computability degree of real numbers arising as $L^2$-Betti numbers or $L^2$-torsion of groups, parametrised over the Turing degree of the word problem.