There is the general principle to consider a classical invariant of a closed Riemannian
manifold M and to define its analog for the universal covering M taking the action of the …

Every closed surface admits a geometry of constant curvature, and may be classified
topologically either by its fundamental group or by its Euler characteristic and orientation …

The aim of this paper is to introduce a notion of L2-homology in the context of von Neumann
algebras. Finding a suitable (co) homology theory for von Neumann algebras has been a …

We extend the notion of a purely infinite simple C*-algebra to the context of unital rings, and
we study its basic properties, specially those related to K-Theory. For instance, if $ R $ is a …

We define for arbitrary modules over a finite von Neumann algebra a dimension taking
values in 0, which extends the classical notion of von Neumann dimension for finitely …

The classifying space E (Γ, F) for a family F of subgroups of a group Γ is defined up to Γ-
homotopy as a Γ-CW-complex E (Γ, F) such that E (Γ, F) H is contractible if H belongs to F …

These are notes from a mini-course at the ETH Zurich addressed to faculty and advanced
students. Its purpose was to provide a first acquaintance of the Hilbert space methods in …

In this paper, we study the class of rings that satisfy internal direct sum cancellation with
respect to their 1-sided ideals. These are known to be precisely the rings in which regular …

A group is of type VF if it has a finite-index subgroup which has a finite classifying space. We
construct groups of type VF in which the centralizers of some elements of finite order are not …

We look at the automorphisms of Thompson type groups of piecewise linear
homeomorphisms of the real line or circle that use slopes that are integral powers of a fixed …