Any covering Y ! X of a hyperbolic Riemann surface X of-nite area determines an inclusion of Teichm uller spaces Teich(X) ,! Teich(Y). We show this map is an isometry for the Teichm uller metric if the covering is amenable, and contracting otherwise. In particular , we establish jjjj < 1 for classical Poincar e series (Kra's `Theta conjecture'). The appendix develops the theory of geometric lim...

Suppose Y is a regular covering of a graph X with covering transformation group π = Z. This paper gives an explicit formula for the L zeta function of Y and computes examples. When π = Z, the L zeta function is an algebraic function. As a consequence it extends to a meromorphic function on a Riemann surface. The meromorphic extension provides a setting to generalize known properties of zeta fun...

Suppose Y is a regular covering of a graph X with covering transformation group π = Z. This paper gives an explicit formula for the L2 zeta function of Y and computes examples. When π = Z, the L2 zeta function is an algebraic function. As a consequence it extends to a meromorphic function on a Riemann surface. The meromorphic extension provides a setting to generalize known properties of zeta f...

Earlier work on Delaunay triangulation of point sets on the 2D flat torus, which is locally isometric to the Euclidean plane, was based on lifting the point set to a locally isometric 9-sheeted covering space of the torus [28, 20, 12, 11]. Under mild conditions the Delaunay triangulation of the lifted point set, consisting of 9 copies of the input set, projects to the Delaunay triangulation of ...

An ordinary voltage graph embedding in a surface encodes a certain kind of highly symmetric covering space of that surface. Given an ordinary voltage graph embedding of a graph G in a surface with voltage group A and a connected subgraph H of G, we define special subgroups of A that depend on H and show how cosets of these groups in A can be used to find topological information concerning the d...

Rough set theory provides a systematic way for rule extraction, attribute reduction and knowledge classification in information systems. Some measurements are important in rough sets. For example, information entropy, knowledge dependency are useful in attribute reduction algorithms. This paper proposes the concepts of the lower and upper covering numbers to establish measurements in covering-b...