Some ball-quotient orbifolds are related by covering maps. We exploit these coverings to find infinitely many orbifolds on P uniformized by the complex 2-ball B2 and some orbifolds over K3 surfaces uniformized by B2. We also give, along with infinitely many reducible examples, an infinite series of irreducible curves along which P is uniformized by the product of 1-balls B1× B1.

We study finite foldable cubical complexes of nonpositive curvature (in the sense of A.D. Alexandrov). We show that such a complex X admits a graph of spaces decomposition. It is also shown that when dimX = 3, X contains a closed rank one geodesic in the 1-skeleton unless the universal cover of X is isometric to the product of two CAT(0) cubical complexes. AMS Classification 20F65, 20F67; 53C20

We consider holomorphic maps f : U → U for a hyperbolic domain U in the complex plane, such that the iterates of f converge to a boundary point ζ of U . By a previous result of the authors, for such maps there exist nice absorbing domains W ⊂ U . In this paper we show that W can be chosen to be simply connected, if f has parabolic I type in the sense of the Baker–Pommerenke–Cowen classification...

An irreducible open 3-manifold W is R-irreducible if it contains no non-trivial planes, i.e. given any proper embedded plane Π in W some component of W −Π must have closure an embedded halfspace R × [0,∞). In this paper it is shown that if M is a connected, P-irreducible, open 3-manifold such that π1(M) is finitely generated and the universal covering space M̃ of M is R-irreducible, then either ...

Let M be a closed hyperbolic three manifold. We construct closed surfaces that map by immersions into M so that for each, one the corresponding mapping on the universal covering spaces is an embedding, or, in other words, the corresponding induced mapping on fundamental groups is an injection.

The fact that flat principal circle bundles are characterized by having zero real Euler classes has proved important in recent years in understanding whether total spaces of vector bundles over nonnegatively curved manifolds must support metrics with nonnegative curvature as well (see Theorem 6.3 and the discussion afterwards). Unfortunately, the proofs of this fact of which we are aware use ei...

In this work we propose a temporal extension to the Parsimonious Covering Theory (PCT). PCT provides a theoretical foundation for the diagnostic reasoning process as an abductive reasoning based associations between causes with their consequences. Our temporal extension of PCT allows one to associate to a disease a temporal evolution of its symptoms. The elimination of temporally inconsistent h...

where r = ∫ Rdμ/ ∫ dμ is the average scalar curvature (R is the scalar curvature) and Ric is the Ricci curvature tensor of h. Hamilton then spectacularly illustrated the success of this method by proving, when n = 3, that if the initial Riemannian metric has strictly positive Ricci curvature it evolves through time to a positively curved Einstein metric h∞ on M . And, because n = 3, such a Riem...

In topology, the notions of the fundamental group and the universal cover are closely intertwined. By importing usual notions from topology into the algebraic and arithmetic setting, we construct a fundamental group family from a universal cover, both of which are schemes. A geometric fiber of the fundamental group family (as a topological group) is canonically the étale fundamental group. The ...

A brief proof of the existence of an equilibrium in incomplete markets is given for regular economies (Theorem 1) ; a robust example of such economies is provided . Theorem 2 establishes that the manifold fl of global pseudo-equilibria is a fiber bundle with the topological structure of a oneor two-fold covering space of G k . ", the space of k planes in R", where k is the number of assets in t...