This paper gives a proof that the universal cover of a closed 3-manifolds built from three π1-injective handlebodies is homeomorphic to R .

We prove that the set of homotopy classes of the paths in a topological ring is a ring object (called ring groupoid). Using this concept we show that the ring structure of a topological ring lifts to a simply connected covering space.

The purpose of this note is to use covering space theory to construct new examples of buildings. On the level of Coxeter systems, this contsruction was described previously in Davis [4]. It goes as follows. Start with a Coxeter system (W ′, S). Change some m(s, t)’s in its Coxeter matrix from integers ≥ 2 to the symbol ∞ . This defines a new Coxeter system (W, S). Suppose C′ is a building of ty...

This article contains a new argument which proves vanishing of the first cohomology for negative vector bundles over a complex projective variety if the rank of the bundle is smaller than the dimension of the base. Similar argument is applied to the construction of holomorphic functions on the universal covering of the complex projective variety .

This paper describes certain properties of the fundamental group of the shrinking wedge of circles. Covering space theory is an inadequate tool since the shrinking wedge of circles is not semi-locally simply connected. We conclude with the fact that the shrinking wedge of circles is not homotopy equivalent to the wedge product of a countable number of circles.

In this paper, three types of (philosophical, optimistic and pessimistic) multigranulation single valued neutrosophic (SVN) covering-based rough set models are presented, and these three models are applied to the problem of multi-criteria group decision making (MCGDM).Firstly, a type of SVN covering-based rough set model is proposed.Based on this rough set model, three types of mult...

In this note we show that for any hyperbolic surface S, the number of geodesics of length bounded above by L in the mapping class group orbit of a fixed closed geodesic γ with a single double point is asymptotic to Ldim(Teichmuller space of S.). Since closed geodesics with one double point fall into a finite number of M≀⌈(S) orbits, we get the same asympotic estimate for the number of such geod...

We construct a relative Chow-Künneth decomposition for a conic bundle over a surface such that the middle projector gives the Prym variety of the associated double covering of the discriminant of the conic bundle. This gives a refinement (up to an isogeny) of Beauville’s theorem on the relation between the intermediate Jacobian of the conic bundle and the Prym variety of the double covering.