We provide a proof for an inequality between volume and LBetti numbers of aspherical manifolds for which Gromov outlined a strategy based on general ideas of Connes. The implementation of that strategy involves measured equivalence relations, Gaboriau’s theory of L-Betti numbers of R-simplicial complexes, and other themes of measurable group theory. Further, we prove new vanishing theorems for ...

This is a survey on known results and open problems about closed aspherical manifolds, i.e., connected closed manifolds whose universal coverings are contractible. Many examples come from certain kinds of non-positive curvature conditions. The property aspherical, which is a purely homotopy theoretical condition, has many striking implications about the geometry and analysis of the manifold or ...

It is very important to improve machining efficiency and ensure manufacture quality through testing NC program of aspherical elements machining with simulation software. For ultra -precision NC machining tool, we analyzed the tool path of ultra-precision grind for aspherical elements, edited a simulation software of the path, got a structural chart of the software, analyzed some important modul...

It is shown that Poincare* duality groups which satisfy the maximal condition on centralisers have a canonical decomposition as the fundamental group of a finite graph of groups in which the edge groups are polycyclic-by-finite. The results give useful information only when there are large polycyclic subgroups. Since 3-manifolds groups satisfy Max-c, the results provide a purely grouptheoretic ...

The main goal of this paper is to give the first examples of equivariant aspherical Poincaré complexes, that are not realized by group actions on closed aspherical manifolds M . These will also provide new counterexamples to the Nielsen realization problem about lifting homotopy actions of finite groups to honest group actions. Our examples show that one cannot guarantee that a given action of ...

The main goal of this paper is to give the first examples of equi-variant aspherical Poincare complexes, that are not realized by group actions on closed aspherical manifolds M. These will also provide new counterexamples to the Nielsen realization problem about lifting homotopy actions of finite groups to honest group actions. Our examples show that one cannot guarantee that a given action of ...

Introduction. A space is aspherical if its universal cover is contractible. Examples of aspherical spaces occur in differential geometry (as complete Riemannian manifolds of nonpositive sectional curvature), in Lie groups (as Γ\G/K where G is a Lie group, K is a maximal compact subgroup and Γ is a discrete torsion-free subgroup), in 3-manifold theory and as certain 2-dimensional cell complexes....

In this paper, Problem 4.17 on R. Kirby’s problem list is solved by constructing infinitely many aspherical 4-manifolds that are homology 4-