Let M̃ → M be a holomorphic (unbranched) covering map between two compact complex manifolds, with b2(M̃) = 1. We prove that if M̃ and M both admit regular Kähler forms ω̃ and ω respectively then, up to homotheties, (M̃, ω̃) and (M, ω) are biholomorphically isometric.

We study the topology of codimension one taut foliations of closed orientable 3-manifolds which are smooth along the leaves. In particular, we focus on the lifts of these foliations to the universal cover, specifically when any set of leaves corresponding to nonseparable points in the leaf space can be totally ordered. We use the structure of branching in the lifted foliation to find conditions...

We consider locally symmetric manifolds with a fixed universal covering, and construct for each such manifold M a simplicial complex R whose size is proportional to the volume of M . When M is non-compact, R is homotopically equivalent to M , while when M is compact, R is homotopically equivalent to M \ N , where N is a finite union of submanifolds of fairly smaller dimensions. This expresses h...

In this paper we shall study homomorphisms p: W — Y on minimal transformation groups. We shall prove, in the case that W and Y are metrizable, that W is a finite (iV-to-1) extension of Y if and only if W is an Nfold covering space of Y and pisa covering map. This result places no further restrictions on the acting group. We shall then use this characterization to investigate the question of lif...

If p : E → B is a continuous surjection between completely regular spaces E and B, we may apply the Stone-Čech compactification functor β to obtain a surjection βp : βE → βB. It is well-known that if E = B × F where F is a finite set and p is projection on the first factor, then βE = βB × βF , and βp is again projection on the first factor. In this paper, we apply β to an n-fold covering map, t...

4-branes that wrap the long and short fundamental 1-cycles of a rectangular toroidal orbifold T 2 /(Z2) 3 , which has Planck-scale compactification radii, intersect after 43 and 109 wrappings, respectively, in a 3-brane upon which the scale factor, equal to a power of the inverse of compactification length, has precisely the same value when measured parallel to either of the fundamental 1-cycle...

We show that if a knot exterior satisfies certain conditions, then it has finite cyclic coverings with arbitrarily large numbers of nontrivial algebraic components in their SL2(C)-character varieties (Theorem A). As an example, these conditions hold for hyperbolic punctured torus bundles over the circle (Theorem B). We investigate in more detail the finite cyclic covers of the figure-eight knot...

Given a set of m identical bins of size 1, the online input consists of a (potentially, infinite) stream of items in (0, 1]. Each item is to be assigned to a bin upon arrival. The goal is to cover all bins, that is, to reach a situation where a total size of items of at least 1 is assigned to each bin. The cost of an algorithm is the sum of all used items at the moment when the goal is first fu...