For a closed orientable surface S, any map f : S→S whose n-th power is homotopic to the identity, is homotopic to a homeomorphism g of S of order n. This famous theorem of Nielsen is known to fail in general for aspherical manifolds. In this paper, for model aspherical manifolds M associated to a finitely extendable set of data, we, however, present a weaker version of Nielsen’s result. We show...

When an asymmetric bubble collapses it generally produces a well defined high velocity jet. This is remarkable because one might expect such a collapse to produce a complex or chaotic flow rather than an ordered one. I present a dimensional argument for the ubiquity of jets from collapsing bubbles, and model the aspherical collapse of a bubble with pieces of Rayleigh’s solution for spherical co...

The results of inelastic neutron scattering provide a solution for the crystal field level scheme in PrOs4Sb12, in which the ground state in the cubic crystal field potential of T(h) symmetry is a Gamma(1) singlet. The conduction electron mass enhancement is consistent with inelastic exchange scattering, and we propose that inelastic quadrupolar, or aspherical Coulomb, scattering is responsible...

We construct a spectral sequence for L-type cohomology groups of discrete measured groupoids. Based on the spectral sequence, we prove the Hopf-Singer conjecture for aspherical manifolds with poly-surface fundamental groups. More generally, we obtain a permanence result for the Hopf-Singer conjecture under taking fiber bundles whose base space is an aspherical manifold with poly-surface fundame...

Given any group Γ, there is an aspherical CW -complex BΓ (also denoted by K(Γ, 1)) with fundamental group Γ; moreover, BΓ is unique up to homotopy equivalence (cf. [Hu]). BΓ is called the classifying space of Γ. (BΓ is also called an Eilenberg-MacLane space for Γ.) So, the theory of aspherical CW -complexes, up to homotopy, is identical with the theory of groups. This point of view led to the n...

We use numerical simulations to study the crystallization of monodisperse systems of hard aspherical particles. We find that particle shape and crystallizability can be easily related to each other when particles are characterized in terms of two simple and experimentally accessible order parameters: one based on the particle surface-to-volume ratio and the other on the angular distribution of ...

A theorem of Gromov says that a complete finite volume Riemannian manifold of bounded negative curvature is the interior of a compact manifold with boundary. If, in addition, the curvature is bounded away from zero then the boundary is an aspherical manifold with virtually nilpotent fundamental group. I will discuss examples showing this is no longer true if the curvature is allowed to approach...

We prove a structure theorem for compact aspherical Lorentz manifolds with abundant local symmetry. If M is a compact, aspherical, real-analytic, complete Lorentz manifold such that the isometry group of the universal cover has semisimple identity component, then the local isometry orbits in M are roughly fibers of a fiber bundle. A corollary is that if M has an open, dense, locally homogeneous...