Related papers: L^2-Betti numbers of one-relator groups

The group of 2-by-2 matrices with integer entries and determinant $\pm > 1$ can be identified either with the group of outer automorphisms of a rank two free group or with the group of isotopy classes of homeomorphisms of a 2-dimensional…

Let G be a finitely presented group, and let p be a prime. Then G is 'large' (respectively, 'p-large') if some normal subgroup with finite index (respectively, index a power of p) admits a non-abelian free quotient. This paper provides a…

The so-called Atiyah conjecture states that the von Neumann dimensions of the L2-homology modules of free G-CW-complexes belong to a certain set of rational numbers, depending on the finite subgroups of G. In this article we extend this…

We study the asymptotic growth of homology groups and the cellular volume of classifying spaces as one passes to normal subgroups $G_n<G$ of increasing finite index in a fixed finitely generated group $G$, assuming $\bigcap_n G_n =1$. We…

In this paper, we investigate left invariant Riemannian metrics on Lie groups with one and two-dimensional commutator subgroups. We explicitly provide the Levi-Civita connection, sectional curvature, and Ricci curvature, and we give…

We prove that norm continuous derivations from a von Neumann algebra into the algebra of operators affiliated with its tensor square are automatically continuous for both the strong operator topology and the measure topology. Furthermore,…

We study gradings by noncommutative groups on finite dimensional Lie algebras over an algebraically closed field of characteristic zero. It is shown that if $L$ is gradeg by a non-abelian finite group $G$ then the solvable radical $R$ of…

We investigate an analogue of the L^2-Betti numbers for amenable linear subshifts. The role of the von Neumann dimension shall be played by the topological entropy.

Associated to every group with a weak spherical Tits system of rank n+1 with an appropriate rank n subgroup, we construct a relative spectral sequence involving group homology of Levi subgroups of both groups. Using the fact that such Levi…

A beautifully simple free generating set for the commutator subgroup of a free group was constructed by Tomaszewski. We give a new geometric proof of his theorem, and show how to give a similar free generating set for the commutator…

The algebraic $L$-groups $L_*(\A,X)$ are defined for an additive category $\A$ with chain duality and a $\Delta$-set $X$, and identified with the generalized homology groups $H_*(X;\LL_{\bullet}(\A))$ of $X$ with coefficients in the…

The cohomology ring of the moduli space of stable holomorphic vector bundles of rank n and degree d over a Riemann surface of genus g>1 has a standard set of generators when n and d are coprime. When n=2 the relations between these…

A left-order on a group $G$ is a total order $<$ on $G$ such that for any $f$, $g$ and $h$ in $G$ we have $f < g \Leftrightarrow hf < hg$. We construct a finitely generated subgroup $G$ of $\operatorname{Homeo} (I^2;\delta I^2)$, the group…

A class of one-relator groups such that every group in the class is determined by a triple of integers and is an HNN-extension of some Baumslag -- Solitar group is considered. A criterion for two groups in this class to be isomorphic and…

We establish a connection between Dixmier's unitarisability problem and the expected degree of random forests on a group. As a consequence, a residually finite group is non-unitarisable if its first L2-Betti number is non-zero or if it is…

The one-skeleton of a G-manifold M is the set of points p in M where $\dim G_p \geq \dim G -1$; and M is a GKM manifold if the dimension of this one-skeleton is 2. Goresky, Kottwitz and MacPherson show that for such a manifold this…

We initiate the study of the $L^2$-Betti numbers of group-theoretic Dehn fillings. For a broad class of virtually special groups $G$, we prove that the $L^2$-Betti numbers of sufficiently deep Dehn fillings $\overline{G}$ are equal to those…

Let X be a building of uniform thickness q+1. L^2-Betti numbers of X are reinterpreted as von-Neumann dimensions of weighted L^2-cohomology of the underlying Coxeter group. The dimension is measured with the help of the Hecke algebra. The…

We examine second bounded cohomology and mod p homology in finite index subgroups of 1-relator groups and groups with a presentation of deficiency at least one. We use this to determine exactly which 1-relator groups are boundedly…

Let $M(d,\chi)$ with $(d,\chi)=1$ be the moduli space of semistable sheaves on $\mathbb{P}^2$ supported on curves of degree $d$ and with Euler characteristic $\chi$. The cohomology ring $H^*(M(d,\chi),\mathbb{Z})$ of $M(d,\chi)$ is…