In 1966, Michael [11] introduced the concept of compact-covering maps. Since many important kinds of maps are compact-covering, such as closed maps on paracompact spaces, much work has been done to seek the characterizations of metric spaces under various compact-covering maps, for example, compact-covering (open) s-maps, pseudosequence-covering (quotient) s-maps, sequence-covering (quotient) s...

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 consider two-dimensional Yang-Mills theories on arbitrary Riemann surfaces. We introduce a generalized Yang-Mills action, which coincides with the ordinary one on flat surfaces but differs from it in its coupling to two-dimensional gravity. The quantization of this theory in the unitary gauge can be consistently performed taking into account all the topological sectors arising from the gauge...

Is it possible to find a formula expressing the Nielsen number N( f ) by the numbers N( ̃ f ) where ̃ f runs the set of all lifts? Such a formula seems very desirable since the difficulty of computing the Nielsen number often depends on the size of the fundamental group. Since π1 ̃ X ⊂ π1X , the computation of N( ̃ f ) may be simpler. We will translate this problem to algebra. The main result of th...

We consider Thurston maps, i.e., branched covering maps f : S → S that are postcritically finite. It is shown that a Thurston map f is expanding (in a suitable sense) if and only if some iterate F = f is semi-conjugate to z : S → S, where d = deg F . More precisely, for such an F we construct a Peano curve γ : S → S (onto), such that F ◦ γ(z) = γ(z) (for all z ∈ S).

In this paper we develop analysis of the monopole maps over universal covering space a compact four manifold. We induce property on local properness map under condition closeness AHS complex. particular construct higher degree when linearized equation is isomorphic, which induces homomorphism between K group C^* algebras. It involves non linear space, related to L^p cohomology. also obtain vari...